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 Calder?n?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.
Function Classes on the Unit Disc Ebook
An Introduction
By: Miroslav Pavlovi?
Publisher:
De Gruyter
Print ISBN: 9783110281231, 3110281236
eText ISBN: 9783110281903, 3110281902
Edition: 1st
Copyright year: 2014
Format: PDF
Available from $ 182.00 USD
SKU: 9783110281903
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