Date of Award
2014
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Sagher, Yoram
Abstract
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.
Extent
72 p.
Recommended Citation
Grigoriev, Stepan M., "General monotonicity, interpolation of operators, and applications" (2014). Electronic Theses and Dissertations 2010 - 2019. 1016.
https://digitalcommons.fau.edu/etd_general_6/1016
Identifier
FA00004290
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2014.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.