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General monotonicity, interpolation of operators, and applications

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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
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
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
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.