Function classes on the unit disc : an introduction /
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 inte...
| Main Author: | |
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| Corporate Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin :
De Gruyter,
[2014]
Berlin ; Boston : [2013] |
| Series: | De Gruyter studies in mathematics
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| Subjects: |
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| 100 | 1 | |a Pavlović, Miroslav | |
| 100 | 1 | |a Pavlović, Miroslav, |e author |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Function classes on the unit disc : |b an introduction / |c Miroslav Pavlović |
| 264 | 1 | |a Berlin : |b De Gruyter, |c [2014] | |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2013] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (449 pages) | ||
| 300 | |a 1 online resource (463 pages) | ||
| 336 | |a text |2 rdacontent | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |2 rdacarrier | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a De Gruyter Studies in Mathematics , |x 0179-0986 ; |v 52 | |
| 490 | 1 | |a De Gruyter studies in mathematics | |
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Contents -- |t 1. The Poisson integral and Hardy spaces -- |t 2. Subharmonic functions and Hardy spaces -- |t 3. Subharmonic behavior and mixed norm spaces -- |t 4. Taylor coefficients with applications -- |t 5. Besov spaces -- |t 6. The dual of H1 and some related spaces -- |t 7. Littlewood-Paley theory -- |t 8. Lipschitz spaces of first order -- |t 9. Lipschitz spaces of higher order -- |t 10. One-to-one mappings -- |t 11. Coefficients multipliers -- |t 12. Toward a theory of vector-valued spaces -- |t A. Quasi-Banach spaces -- |t B. Interpolation and maximal functions -- |t Bibliography -- |t Index |
| 506 | |a Access restricted by licensing agreement | ||
| 506 | |a Restricted for use by site license. | ||
| 520 | |a 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 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 | ||
| 530 | |a Issued also in printing | ||
| 538 | |a Mode of access: Internet via World Wide Web | ||
| 546 | |a In English | ||
| 588 | |a Description based on online resource; title from PDF title page (ebrary, viewed March 11, 2014) | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) | |
| 590 | |a Access is available to the Yale community | ||
| 650 | 0 | |a Banach spaces | |
| 650 | 0 | |a Function spaces | |
| 650 | 0 | |a Functional analysis | |
| 650 | 0 | |a Hardy spaces | |
| 650 | 0 | |a Lipschitz spaces | |
| 650 | 0 | |a Poisson integral formula | |
| 650 | 4 | |a Bergman spaces | |
| 650 | 4 | |a H^p spaces | |
| 650 | 4 | |a Hardy spaces | |
| 650 | 4 | |a L^p spaces | |
| 650 | 4 | |a Quasinormed spaces | |
| 650 | 4 | |a harmonic functions | |
| 650 | 7 | |a MATHEMATICS / Functional Analysis |2 bisacsh | |
| 653 | |a Bergman Space | ||
| 653 | |a Besov-Lipschitz Space | ||
| 653 | |a Bounded Mean Oscillation | ||
| 653 | |a Hardy Space | ||
| 653 | |a Littlewood-Paley g-Function | ||
| 700 | 1 | |a Pavlović, Miroslav, |e contributor |4 ctb |4 https://id.loc.gov/vocabulary/relators/ctb | |
| 710 | 2 | |a De Gruyter | |
| 773 | 0 | |a De Gruyter Book Archive | |
| 776 | 0 | |c print |z 9783110281231 | |
| 797 | 2 | |a ebrary | |
| 830 | 0 | |a De Gruyter studies in mathematics | |
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