Current Search: Nonsmooth optimization (x)
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Title
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General monotonicity, interpolation of operators, and applications.
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Creator
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Grigoriev, Stepan M., Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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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...
Show moreAssume 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.
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Date Issued
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2014
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PURL
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http://purl.flvc.org/fau/fd/FA00004290, http://purl.flvc.org/fau/fd/FA00004290
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Subject Headings
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Combinatorial optimization, Differential dynamical systems, Functions of complex variables, Inequalities (Mathematics), Nonsmooth optimization
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Format
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Document (PDF)
