Function Classes on the Unit Disc: An Introduction Contributor(s): Pavlovic, Miroslav (Author) |
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ISBN: 3110281236 ISBN-13: 9783110281231 Publisher: de Gruyter OUR PRICE: $228.00 Product Type: Hardcover - Other Formats Published: December 2013 |
Additional Information |
BISAC Categories: - Mathematics | Reference - Mathematics | Mathematical Analysis - Mathematics | Functional Analysis |
Dewey: 515.7 |
Series: de Gruyter Studies in Mathematics |
Physical Information: 1" H x 6.69" W x 9.61" (2.06 lbs) 462 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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 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. |