An application of interpolation theory to Fourier series

DOI10.4064/sm-41-2-169-181zbMath0258.42004OpenAlexW777747548MaRDI QIDQ5673864

Yoram Sagher

Publication date: 1972

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/217604

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (22)

Weighted Fourier inequalities and boundedness of variation ⋮ Norm inequalities for certain classes of functions and their Fourier transforms ⋮ Functions with general monotone Fourier coefficients ⋮ Fourier-Price coefficients of class GM and best approximations of functions in the Lorentz space \(L_{p\theta}[0, 1)\), \(1<p<+\infty\), \(1<\theta<+\infty\) ⋮ Multiplicative convolutions of functions from Lorentz spaces and convergence of series of Fourier-Vilenkin coefficients ⋮ Interpolation of linear operators ⋮ General monotonicity and interpolation of operators ⋮ Piecewise general monotone functions and the Hardy-Littlewood theorem ⋮ Spaces of Lorentz Multipliers ⋮ Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations ⋮ Series in multiplicative systems in Lorentz spaces ⋮ Cosine and sine series with generalized monotone coefficients in Lorentz spaces ⋮ On summability of Fourier coefficients of functions from Lebesgue space ⋮ General monotone sequences and trigonometric series ⋮ Function cones and interpolation ⋮ On the spectra of a Hardy kernel ⋮ Integrability conditions for the Fourier transform ⋮ Paley inequality for Bellman transform of multiple Fourier series ⋮ The Hardy-Littlewood theorem for the cosine series in a symmetric space ⋮ Monomial convergence on \(\ell_r\) ⋮ The Boas problem on Hankel transforms ⋮ Interpolation of cones and shape-preserving approximation

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