Integrability theorems for Fourier series

DOI10.1215/S0012-7094-66-03326-6zbMath0136.36501OpenAlexW2006410320MaRDI QIDQ2521656

Stephen Wainger, Richard Askey

Publication date: 1966

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-66-03326-6

zbMATH Keywords

approximation and series expansion

Related Items (31)

Weighted integrability of double series with respect to multiplicative systems ⋮ Weighted Fourier inequalities and boundedness of variation ⋮ Norm inequalities for some orthogonal series ⋮ On some variants of Hardy's inequality ⋮ On weighted integrability of double cosine series ⋮ Convergence of trigonometric series with general monotone coefficients ⋮ Trigonometric series with general monotone coefficients ⋮ On fourier series with positive coefficients ⋮ On weighted \(L^p\) integrability of functions defined by trigonometric series ⋮ On a new class of Hardy type inequalities ⋮ Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients ⋮ Applications of MVBV condition in \(L^1\) integrability ⋮ General monotonicity and interpolation of operators ⋮ Weighted Fourier inequalities: Boas' conjecture in \({\mathbb{R}}^{n}\) ⋮ On the integrability with weight of trigonometric series ⋮ Mean bounded variation condition and applications in double trigonometric series ⋮ On certain conditions in the theory of series with respect to multiplicative systems ⋮ Estimates of best approximations in integral metrics and Fourier coefficients with respect to multiplicative systems ⋮ Best approximation and moduli of smoothness: Computation and equivalence theorems ⋮ Cosine and sine series with generalized monotone coefficients in Lorentz spaces ⋮ Extended solution of Boas' conjecture on Fourier transforms ⋮ General monotone sequences and trigonometric series ⋮ On the Integrability of Power Series ⋮ On some inequalities for Fourier series ⋮ Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates ⋮ Fourier series with positive coefficients ⋮ Fourier coefficients of positive functions ⋮ Modules of continuity of functions defined by trigonometric series ⋮ Necessary and sufficient conditions for integrability of certain cosine sums ⋮ Some Hardy-type inequalities ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

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