Function Classes on the Unit Disc : : An Introduction / / Miroslav Pavlović.
This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are inte...
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Pavlović, Miroslav, author. aut http://id.loc.gov/vocabulary/relators/aut Function Classes on the Unit Disc : An Introduction / Miroslav Pavlović. Berlin ; Boston : De Gruyter, [2013] ©2014 1 online resource (449 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 52 Frontmatter -- Preface -- Contents -- 1. The Poisson integral and Hardy spaces -- 2. Subharmonic functions and Hardy spaces -- 3. Subharmonic behavior and mixed norm spaces -- 4. Taylor coefficients with applications -- 5. Besov spaces -- 6. The dual of H1 and some related spaces -- 7. Littlewood–Paley theory -- 8. Lipschitz spaces of first order -- 9. Lipschitz spaces of higher order -- 10. One-to-one mappings -- 11. Coefficients multipliers -- 12. Toward a theory of vector-valued spaces -- A. Quasi-Banach spaces -- B. Interpolation and maximal functions -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, α)-maximal theorems and (C, α)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p › 0) and Calderón's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights. It also contains a discussion of analytic functions and lacunary series with values in quasi-Banach spaces with applications to function spaces and composition operators. Sixteen open questions are posed. The reader is assumed to have a good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series. Further information can be found at the author's website at http://poincare.matf.bg.ac.rs/~pavlovic. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Banach spaces. Function spaces. Functional analysis. Poisson integral formula. Bergman spaces. H^p spaces. Hardy spaces. L^p spaces. Quasinormed spaces. harmonic functions. MATHEMATICS / Functional Analysis. bisacsh Bergman Space. Besov-Lipschitz Space. Bounded Mean Oscillation. Hardy Space. Littlewood-Paley g-Function. Pavlović, Miroslav, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 9783110317350 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 9783110317282 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 9783110317275 ZDB-23-DMP print 9783110281231 https://doi.org/10.1515/9783110281903 https://www.degruyter.com/isbn/9783110281903 Cover https://www.degruyter.com/document/cover/isbn/9783110281903/original |
language |
English |
format |
eBook |
author |
Pavlović, Miroslav, Pavlović, Miroslav, |
spellingShingle |
Pavlović, Miroslav, Pavlović, Miroslav, Function Classes on the Unit Disc : An Introduction / De Gruyter Studies in Mathematics , Frontmatter -- Preface -- Contents -- 1. The Poisson integral and Hardy spaces -- 2. Subharmonic functions and Hardy spaces -- 3. Subharmonic behavior and mixed norm spaces -- 4. Taylor coefficients with applications -- 5. Besov spaces -- 6. The dual of H1 and some related spaces -- 7. Littlewood–Paley theory -- 8. Lipschitz spaces of first order -- 9. Lipschitz spaces of higher order -- 10. One-to-one mappings -- 11. Coefficients multipliers -- 12. Toward a theory of vector-valued spaces -- A. Quasi-Banach spaces -- B. Interpolation and maximal functions -- Bibliography -- Index |
author_facet |
Pavlović, Miroslav, Pavlović, Miroslav, Pavlović, Miroslav, Pavlović, Miroslav, |
author_variant |
m p mp m p mp |
author_role |
VerfasserIn VerfasserIn |
author2 |
Pavlović, Miroslav, Pavlović, Miroslav, |
author2_variant |
m p mp m p mp |
author2_role |
MitwirkendeR MitwirkendeR |
author_sort |
Pavlović, Miroslav, |
title |
Function Classes on the Unit Disc : An Introduction / |
title_sub |
An Introduction / |
title_full |
Function Classes on the Unit Disc : An Introduction / Miroslav Pavlović. |
title_fullStr |
Function Classes on the Unit Disc : An Introduction / Miroslav Pavlović. |
title_full_unstemmed |
Function Classes on the Unit Disc : An Introduction / Miroslav Pavlović. |
title_auth |
Function Classes on the Unit Disc : An Introduction / |
title_alt |
Frontmatter -- Preface -- Contents -- 1. The Poisson integral and Hardy spaces -- 2. Subharmonic functions and Hardy spaces -- 3. Subharmonic behavior and mixed norm spaces -- 4. Taylor coefficients with applications -- 5. Besov spaces -- 6. The dual of H1 and some related spaces -- 7. Littlewood–Paley theory -- 8. Lipschitz spaces of first order -- 9. Lipschitz spaces of higher order -- 10. One-to-one mappings -- 11. Coefficients multipliers -- 12. Toward a theory of vector-valued spaces -- A. Quasi-Banach spaces -- B. Interpolation and maximal functions -- Bibliography -- Index |
title_new |
Function Classes on the Unit Disc : |
title_sort |
function classes on the unit disc : an introduction / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2013 |
physical |
1 online resource (449 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- 1. The Poisson integral and Hardy spaces -- 2. Subharmonic functions and Hardy spaces -- 3. Subharmonic behavior and mixed norm spaces -- 4. Taylor coefficients with applications -- 5. Besov spaces -- 6. The dual of H1 and some related spaces -- 7. Littlewood–Paley theory -- 8. Lipschitz spaces of first order -- 9. Lipschitz spaces of higher order -- 10. One-to-one mappings -- 11. Coefficients multipliers -- 12. Toward a theory of vector-valued spaces -- A. Quasi-Banach spaces -- B. Interpolation and maximal functions -- Bibliography -- Index |
isbn |
9783110281903 9783110494938 9783110238570 9783110238471 9783110637205 9783110317350 9783110317282 9783110317275 9783110281231 |
issn |
0179-0986 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA320 |
callnumber-sort |
QA 3320 P38 42013EB |
url |
https://doi.org/10.1515/9783110281903 https://www.degruyter.com/isbn/9783110281903 https://www.degruyter.com/document/cover/isbn/9783110281903/original |
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Not Illustrated |
doi_str_mv |
10.1515/9783110281903 |
oclc_num |
870589848 |
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AT pavlovicmiroslav functionclassesontheunitdiscanintroduction |
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Function Classes on the Unit Disc : An Introduction / |
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