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Function Classes on the Unit Disc: An Introduction (De Gruyter Studies in Mathematics, 52) - Hardcover
Synopsis
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.
"synopsis" may belong to another edition of this title.
About the Author
Miroslav Pavlovic, University of Belgrade, Serbia.
Review
"In this ambitious book, the author treats a number of topics from the theory of functions and function spaces on the unit disc in the complex plane. The selection of topics is far ranging, and includes both classical and modern ideas. Many of his proofs are new or unusual, and many of his ideas and presentations appear here in book form for the first time." -- Steven G. Krantz, Mathematical Reviews
"[...] this is a well-written and detailed text with concise proofs. Graduate students and researchers who are pursuing research in harmonic or holomorphic function theory of one or several variables will find this book to be an excellent addition to their personal library." -- Manfred Stoll, Zentralblatt für Mathematik
"About this title" may belong to another edition of this title.
- PublisherDe Gruyter
- Publication date2013
- ISBN 10 3110281236
- ISBN 13 9783110281231
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages462
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Function Classes on the Unit Disc : An Introduction
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In this ambitious book, the author treats a number of topics from the theory of functions and function spaces on the unit disc in the complex plane. The selection of topics is far ranging, and includes both classical and modern ideas. Many of his proofs. Seller Inventory # 4456657
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 poincare.matf.bg.ac.rs/~pavlovic. Seller Inventory # 9783110281231
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 poincare.matf.bg.ac.rs/~pavlovic. 464 pp. Englisch. Seller Inventory # 9783110281231
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