Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces

We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) a...
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Gespeichert in:

Autor*in:	Dzhabrailov Malik S. [verfasserIn] Khaligova Sevinc Z. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space

Übergeordnetes Werk:	In: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica - Sciendo, 2008, 21(2013), 2, Seite 111-130
Übergeordnetes Werk:	volume:21 ; year:2013 ; number:2 ; pages:111-130

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.2478/auom-2013-0026

Katalog-ID:	DOAJ023445610

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245	1	0	\|a Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
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520			\|a We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).
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allfields	10.2478/auom-2013-0026 doi (DE-627)DOAJ023445610 (DE-599)DOAJ1e8668ef5d0842cdb9c0a6c8fd6cb843 DE-627 ger DE-627 rakwb eng QA1-939 Dzhabrailov Malik S. verfasserin aut Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics Khaligova Sevinc Z. verfasserin aut In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica Sciendo, 2008 21(2013), 2, Seite 111-130 (DE-627)535187017 (DE-600)2375753-X 18440835 nnns volume:21 year:2013 number:2 pages:111-130 https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 kostenfrei https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/toc/1844-0835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2013 2 111-130
spelling	10.2478/auom-2013-0026 doi (DE-627)DOAJ023445610 (DE-599)DOAJ1e8668ef5d0842cdb9c0a6c8fd6cb843 DE-627 ger DE-627 rakwb eng QA1-939 Dzhabrailov Malik S. verfasserin aut Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics Khaligova Sevinc Z. verfasserin aut In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica Sciendo, 2008 21(2013), 2, Seite 111-130 (DE-627)535187017 (DE-600)2375753-X 18440835 nnns volume:21 year:2013 number:2 pages:111-130 https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 kostenfrei https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/toc/1844-0835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2013 2 111-130
allfields_unstemmed	10.2478/auom-2013-0026 doi (DE-627)DOAJ023445610 (DE-599)DOAJ1e8668ef5d0842cdb9c0a6c8fd6cb843 DE-627 ger DE-627 rakwb eng QA1-939 Dzhabrailov Malik S. verfasserin aut Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics Khaligova Sevinc Z. verfasserin aut In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica Sciendo, 2008 21(2013), 2, Seite 111-130 (DE-627)535187017 (DE-600)2375753-X 18440835 nnns volume:21 year:2013 number:2 pages:111-130 https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 kostenfrei https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/toc/1844-0835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2013 2 111-130
allfieldsGer	10.2478/auom-2013-0026 doi (DE-627)DOAJ023445610 (DE-599)DOAJ1e8668ef5d0842cdb9c0a6c8fd6cb843 DE-627 ger DE-627 rakwb eng QA1-939 Dzhabrailov Malik S. verfasserin aut Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics Khaligova Sevinc Z. verfasserin aut In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica Sciendo, 2008 21(2013), 2, Seite 111-130 (DE-627)535187017 (DE-600)2375753-X 18440835 nnns volume:21 year:2013 number:2 pages:111-130 https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 kostenfrei https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/toc/1844-0835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2013 2 111-130
allfieldsSound	10.2478/auom-2013-0026 doi (DE-627)DOAJ023445610 (DE-599)DOAJ1e8668ef5d0842cdb9c0a6c8fd6cb843 DE-627 ger DE-627 rakwb eng QA1-939 Dzhabrailov Malik S. verfasserin aut Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics Khaligova Sevinc Z. verfasserin aut In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica Sciendo, 2008 21(2013), 2, Seite 111-130 (DE-627)535187017 (DE-600)2375753-X 18440835 nnns volume:21 year:2013 number:2 pages:111-130 https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 kostenfrei https://doi.org/10.2478/auom-2013-0026 kostenfrei https://doaj.org/toc/1844-0835 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2013 2 111-130
language	English
source	In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica 21(2013), 2, Seite 111-130 volume:21 year:2013 number:2 pages:111-130
sourceStr	In Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica 21(2013), 2, Seite 111-130 volume:21 year:2013 number:2 pages:111-130
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space Mathematics
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container_title	Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
authorswithroles_txt_mv	Dzhabrailov Malik S. @@aut@@ Khaligova Sevinc Z. @@aut@@
publishDateDaySort_date	2013-01-01T00:00:00Z
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callnumber-first	Q - Science
author	Dzhabrailov Malik S.
spellingShingle	Dzhabrailov Malik S. misc QA1-939 misc anisotropic riesz potential misc anisotropic fractional maximal function misc anisotropic modified morrey space misc anisotropic bmo space misc Mathematics Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
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topic_title	QA1-939 Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space
topic	misc QA1-939 misc anisotropic riesz potential misc anisotropic fractional maximal function misc anisotropic modified morrey space misc anisotropic bmo space misc Mathematics
topic_unstemmed	misc QA1-939 misc anisotropic riesz potential misc anisotropic fractional maximal function misc anisotropic modified morrey space misc anisotropic bmo space misc Mathematics
topic_browse	misc QA1-939 misc anisotropic riesz potential misc anisotropic fractional maximal function misc anisotropic modified morrey space misc anisotropic bmo space misc Mathematics
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title	Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
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title_full	Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
author_sort	Dzhabrailov Malik S.
journal	Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
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author_browse	Dzhabrailov Malik S. Khaligova Sevinc Z.
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title_sort	necessary and sufficient conditions for the boundedness of the anisotropic riesz potential in anisotropic modified morrey spaces
callnumber	QA1-939
title_auth	Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
abstract	We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).
abstractGer	We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).
abstract_unstemmed	We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/\|σ\|≤1-1/q≤α/(\|σ\|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/\|σ\| ≤ 1/p-1/q≤α ((1-b) \|σ\|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).
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title_short	Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
url	https://doi.org/10.2478/auom-2013-0026 https://doaj.org/article/1e8668ef5d0842cdb9c0a6c8fd6cb843 https://doaj.org/toc/1844-0835
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doi_str	10.2478/auom-2013-0026
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up_date	2024-07-03T17:39:12.819Z
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Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces

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