Function Classes on the Unit Disc
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, a)-maximal theorems and (C, a)-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.
Autor: | Pavlovic, Miroslav |
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ISBN: | 9783110281231 |
Auflage: | 1 |
Sprache: | Englisch |
Seitenzahl: | 449 |
Produktart: | Gebunden |
Verlag: | De Gruyter |
Veröffentlicht: | 12.12.2013 |
Untertitel: | An Introduction |
Schlagworte: | Bergman Space Bergman spaces Besov-Lipschitz Space Bounded Mean Oscillation H^p spaces Hardy Space Hardy spaces L^p spaces Quasinormed spaces harmonic functions |
Miroslav Pavlovic, University of Belgrade, Serbia.