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, ?)-maximal theorems and (C, ?)-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.
| ISBN: | 9783110281231 |
| Publication date: | 12th December 2013 |
| Author: | Miroslav PavloviÔc |
| Publisher: | De Gruyter |
| Format: | Hardback |
| Pagination: | 462 pages |
| Series: | De Gruyter Studies in Mathematics |
| Genres: |
Reference works Complex analysis, complex variables Functional analysis and transforms |
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, ?)-maximal theorems and (C, ?)-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.
Function Classes on the Unit Disc features in the following genres: Reference works, Complex analysis, complex variables, Functional analysis and transforms
Hardback. £148.05, down from the £164.50 cover price. Not Available.
Function Classes on the Unit Disc was written by Miroslav PavloviÔc and published by De Gruyter
Function Classes on the Unit Disc has 462 pages
Yes it is part of De Gruyter Studies in Mathematics series
£148.05, reduced from £164.50. Not Available.