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General monotonicity, interpolation of operators, and applications
- Date Issued:
- 2014
- Summary:
- Assume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complex-valued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lp-norm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by Tikhonov, Li yand, Booton and others.The present work continues the generalization of these results.
Title: | General monotonicity, interpolation of operators, and applications. |
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Name(s): |
Grigoriev, Stepan M., author Sagher, Yoram, Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Mathematical Sciences |
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Type of Resource: | text | |
Genre: | Electronic Thesis Or Dissertation | |
Date Created: | 2014 | |
Date Issued: | 2014 | |
Publisher: | Florida Atlantic University | |
Place of Publication: | Boca Raton, Fla. | |
Physical Form: | application/pdf | |
Extent: | 72 p. | |
Language(s): | English | |
Summary: | Assume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complex-valued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lp-norm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by Tikhonov, Li yand, Booton and others.The present work continues the generalization of these results. | |
Identifier: | FA00004290 (IID) | |
Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2014. | |
Collection: | FAU Electronic Theses and Dissertations Collection | |
Note(s): | Includes bibliography. | |
Subject(s): |
Combinatorial optimization Differential dynamical systems Functions of complex variables Inequalities (Mathematics) Nonsmooth optimization |
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Held by: | Florida Atlantic University Libraries | |
Sublocation: | Digital Library | |
Links: | http://purl.flvc.org/fau/fd/FA00004290 | |
Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004290 | |
Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
Host Institution: | FAU | |
Is Part of Series: | Florida Atlantic University Digital Library Collections. |