Projections on $ L^{p} $-spaces of polyanalytic functions

Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m,...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Vasin, A. V. [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	1994

Schlagwörter:	Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain

Anmerkung:	© Plenum Publishing Corporation 1994

Übergeordnetes Werk:	Enthalten in: Journal of mathematical sciences - Kluwer Academic Publishers-Plenum Publishers, 1994, 71(1994), 1 vom: Aug., Seite 2180-2191
Übergeordnetes Werk:	volume:71 ; year:1994 ; number:1 ; month:08 ; pages:2180-2191

Links:	Volltext

DOI / URN:	10.1007/BF02111292

Katalog-ID:	OLC2030736414

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520			\|a Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains.
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allfields	10.1007/BF02111292 doi (DE-627)OLC2030736414 (DE-He213)BF02111292-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vasin, A. V. verfasserin aut Projections on $ L^{p} $-spaces of polyanalytic functions 1994 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1994 Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 71(1994), 1 vom: Aug., Seite 2180-2191 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:71 year:1994 number:1 month:08 pages:2180-2191 https://doi.org/10.1007/BF02111292 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4325 31.00 VZ AR 71 1994 1 08 2180-2191
spelling	10.1007/BF02111292 doi (DE-627)OLC2030736414 (DE-He213)BF02111292-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vasin, A. V. verfasserin aut Projections on $ L^{p} $-spaces of polyanalytic functions 1994 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1994 Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 71(1994), 1 vom: Aug., Seite 2180-2191 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:71 year:1994 number:1 month:08 pages:2180-2191 https://doi.org/10.1007/BF02111292 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4325 31.00 VZ AR 71 1994 1 08 2180-2191
allfields_unstemmed	10.1007/BF02111292 doi (DE-627)OLC2030736414 (DE-He213)BF02111292-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vasin, A. V. verfasserin aut Projections on $ L^{p} $-spaces of polyanalytic functions 1994 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1994 Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 71(1994), 1 vom: Aug., Seite 2180-2191 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:71 year:1994 number:1 month:08 pages:2180-2191 https://doi.org/10.1007/BF02111292 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4325 31.00 VZ AR 71 1994 1 08 2180-2191
allfieldsGer	10.1007/BF02111292 doi (DE-627)OLC2030736414 (DE-He213)BF02111292-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vasin, A. V. verfasserin aut Projections on $ L^{p} $-spaces of polyanalytic functions 1994 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1994 Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 71(1994), 1 vom: Aug., Seite 2180-2191 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:71 year:1994 number:1 month:08 pages:2180-2191 https://doi.org/10.1007/BF02111292 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4325 31.00 VZ AR 71 1994 1 08 2180-2191
allfieldsSound	10.1007/BF02111292 doi (DE-627)OLC2030736414 (DE-He213)BF02111292-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vasin, A. V. verfasserin aut Projections on $ L^{p} $-spaces of polyanalytic functions 1994 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1994 Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. Analytic Function Lebesgue Measure Connected Domain Fundamental Result Smooth Domain Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 71(1994), 1 vom: Aug., Seite 2180-2191 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:71 year:1994 number:1 month:08 pages:2180-2191 https://doi.org/10.1007/BF02111292 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4325 31.00 VZ AR 71 1994 1 08 2180-2191
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author	Vasin, A. V.
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title_sort	projections on $ l^{p} $-spaces of polyanalytic functions
title_auth	Projections on $ L^{p} $-spaces of polyanalytic functions
abstract	Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. © Plenum Publishing Corporation 1994
abstractGer	Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. © Plenum Publishing Corporation 1994
abstract_unstemmed	Abstract The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace $ L_{n,m} $p(Ω) of the space $ L^{p} $(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯$ Z^{m} $∂$ Z^{n} $)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space $ L_{n,m} $P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic $ L^{P} $-functions in Ω is complemented in $ L^{P} $(Ω, σ). This result has been known earlier only for smooth domains. © Plenum Publishing Corporation 1994
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title_short	Projections on $ L^{p} $-spaces of polyanalytic functions
url	https://doi.org/10.1007/BF02111292
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doi_str	10.1007/BF02111292
up_date	2024-07-04T02:52:38.702Z
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