Function Classes on the Unit Disc : : An Introduction / / Miroslav Pavlović.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Pavlović, Miroslav,
• MitwirkendeR: Pavlović, Miroslav,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2013]; ©2014
• Year of Publication: 2013
• Language: English
• Series: De Gruyter Studies in Mathematics , 52
• Physical Description: 1 online resource (449 p.)
• 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
• 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.

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.