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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Superior document: | Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2013] ©2014 |
Year of Publication: | 2013 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
52 |
Online Access: | |
Physical Description: | 1 online resource (449 p.) |
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Other title: | 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 |
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Summary: | 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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110281903 9783110494938 9783110238570 9783110238471 9783110637205 9783110317350 9783110317282 9783110317275 |
ISSN: | 0179-0986 ; |
DOI: | 10.1515/9783110281903 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Miroslav Pavlović. |