Function classes on the unit disc : an introduction / / Miroslav Pavlović

• Autore: Pavlović Miroslav
• Pubblicazione: Berlin : , : De Gruyter, , [2014]; ©2014
• Descrizione fisica: 1 online resource (463 p.)
• Disciplina: 510
• Soggetto topico: Functional analysis
• Soggetto non controllato: Bergman Space; Besov-Lipschitz Space; Bounded Mean Oscillation; Hardy Space; Littlewood-Paley g-Function
• Classificazione: SK 600
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Preface / Pavlović, Miroslav -- 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Function classes on the unit disc
• ISBN: 3-11-028190-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910787601603321
• Lo trovi qui: Univ. Federico II
• Serie: De Gruyter Studies in Mathematics