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

Format:

Book

Author/Creator:

Pavlović, Miroslav.

Series:

De Gruyter Studies in Mathematics

De Gruyter Studies in Mathematics ; 52

Language:

English

Subjects (All):

Functional analysis.

Physical Description:

1 online resource (463 p.)

Edition:

1st ed.

Place of Publication:

Berlin : De Gruyter, [2014]

Language Note:

English

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.

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed March 11, 2014).

ISBN:

9783110281903

3110281902

OCLC:

1002221767