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
Autor*in: |
Vasin, A. V. [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
1994 |
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Schlagwörter: |
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Anmerkung: |
© Plenum Publishing Corporation 1994 |
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Übergeordnetes Werk: |
Enthalten in: Journal of mathematical sciences - Kluwer Academic Publishers-Plenum Publishers, 1994, 71(1994), 1 vom: Aug., Seite 2180-2191 |
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Übergeordnetes Werk: |
volume:71 ; year:1994 ; number:1 ; month:08 ; pages:2180-2191 |
Links: |
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DOI / URN: |
10.1007/BF02111292 |
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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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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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Projections on $ L^{p} $-spaces of polyanalytic functions |
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title_full |
Projections on $ L^{p} $-spaces of polyanalytic functions |
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Vasin, A. V. |
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Journal of mathematical sciences |
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Journal of mathematical sciences |
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1994 |
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2180 |
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Vasin, A. V. |
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71 |
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Aufsätze |
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Vasin, A. V. |
doi_str_mv |
10.1007/BF02111292 |
dewey-full |
510 |
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 |
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https://doi.org/10.1007/BF02111292 |
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2024-07-04T02:52:38.702Z |
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