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General monotonicity, interpolation of operators, and applications

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. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

Identiferoai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_30779
ContributorsGrigoriev, Stepan M. (author), Sagher, Yoram (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Mathematical Sciences
PublisherFlorida Atlantic University
Source SetsFlorida Atlantic University
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation, Text
Format72 p., application/pdf
RightsCopyright © 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., http://rightsstatements.org/vocab/InC/1.0/

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