Weighted Fourier inequalities and boundedness of variation

DOI10.1134/S0081543821010193zbMath1462.42010OpenAlexW3158424045MaRDI QIDQ828609

Sergey Yu. Tikhonov

Publication date: 5 May 2021

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543821010193

zbMATH Keywords

Fourier transformsFourier seriesweighted norm inequalitiesgeneral monotone sequencesHardy-Littlewood type theorems

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities involving other types of functions (26D07)

Related Items (2)

Functions with general monotone Fourier coefficients ⋮ Sparse grid approximation in weighted Wiener spaces

Cites Work

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• Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates
• Weighted Fourier inequalities in Lebesgue and Lorentz spaces
• Weighted Hardy inequalities for decreasing sequences and functions
• Trigonometric series with general monotone coefficients
• Best approximation and moduli of smoothness: Computation and equivalence theorems
• On the transformation of Fourier coefficients of certain classes of functions. II
• Estimates for the norms of integral and discrete operators of Hardy type on cones of quasimonotone functions.
• Weighted Fourier inequalities: New proofs and generalizations.
• Pitt inequalities and restriction theorems for the Fourier transform
• Weighted Fourier inequalities via rearrangements
• Embeddings and characterizations of Lipschitz spaces
• On summability of Fourier coefficients of functions from Lebesgue space
• Weighted norm inequalities for generalized Fourier-type transforms and applications
• The Boas problem on Hankel transforms
• Integrability theorems for Fourier series
• A transplantation theorem for ultraspherical coefficients
• A transplantation theorem for Jacobi coefficients
• An extension of the Hausdorff-Young theorem
• Convergence of trigonometric series with general monotone coefficients
• Theorems on Fourier series and power series
• Reduction theorems for weighted integral inequalities on the cone of monotone functions
• Two-sided weighted Fourier inequalities
• A concept of general monotonicity and applications
• Maximal Functions on Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions
• Interpolation of Linear Operators
• Weighted Norm Inequalities for Certain Integral Operators
• Integrability and continuity of functions represented by trigonometric series: coefficients criteria
• Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions
• Weighted Fourier Transform Inequalities for Radially Decreasing Functions
• Notes on the Theory of Series (XIII): Some New Properties of Fourier Constants
• On the coefficients of multiple Fourier series in $ L_p$-spaces
• Weighted norm inequalities for integral transforms
• Hardy–Littlewood theorems for trigonometric series with general monotone coefficients
• On L^pintegrability and convergence of trigonometric series
• Norm inequalities for some orthogonal series
• Hardy's inequality with weights
• An application of interpolation theory to Fourier series
• Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations
• On the integrability of trigonometric series

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