Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

DOI10.1016/j.jat.2012.05.017zbMath1252.42011arXiv1204.4392OpenAlexW2097575988MaRDI QIDQ714890

Dmitry Gorbachev, Sergey Yu. Tikhonov

Publication date: 11 October 2012

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.4392

zbMATH Keywords

Fourier transformstwo-sided estimatesFourier coefficientsradial functionmoduli of smoothnessPitt's inequalitygeneral monotonicity

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25)

Related Items (23)

Weighted Fourier inequalities and boundedness of variation ⋮ Functions with general monotone Fourier coefficients ⋮ A note on \(K\)-functional, modulus of smoothness, Jackson theorem and Bernstein-Nikolskii-Stechkin inequality on Damek-Ricci spaces ⋮ New estimates for the maximal functions and applications ⋮ Embedding relations of Besov classes under MVBV ⋮ Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients ⋮ Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation ⋮ Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity ⋮ Sparse grid approximation in weighted Wiener spaces ⋮ Boas type and Titchmarsh type theorems for generalized Fourier-Bessel transform ⋮ Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Fourier transforms and fractional Lipschitz and Nikol'skii classes in uniform metric ⋮ Superposition, reduction of multivariable problems, and approximation ⋮ Growth and integrability of Fourier transforms on Euclidean space ⋮ Smoothness of functions and Fourier coefficients ⋮ An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin \(L_2\)-inequality ⋮ Characterising extended Lipschitz type conditions with moduli of continuity ⋮ Reconstruction Operator of Functions from the Sobolev Space ⋮ Decay of Fourier Transforms and Generalized Besov Spaces ⋮ The Boas problem on Hankel transforms ⋮ General types of spherical mean operators and \(K\)-functionals of fractional orders ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations ⋮ Lipschitz and Fourier type conditions with moduli of continuity in rank \(1\) symmetric spaces

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