\(\ell_{1}\)-summability of \(d\)-dimensional Fourier transforms

DOI10.1007/s00365-011-9128-9zbMath1234.42004OpenAlexW2003442101MaRDI QIDQ662809

Ferenc Weisz

Publication date: 13 February 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-011-9128-9

zbMATH Keywords

interpolationFourier transformsHardy spaces\(\ell_{1}-\theta\)-summationp-atom

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) (H^p)-spaces (42B30) Summability in several variables (42B08)

Related Items (5)

Approximation and entropy numbers of embeddings between approximation spaces ⋮ \(\ell _{1}\)-summability of higher-dimensional Fourier series ⋮ Inversion formulas for the continuous wavelet transform ⋮ Weak type inequalities for the \(\ell_1\)-summability of higher dimensional Fourier transforms ⋮ \(\ell_1\)-summability and Lebesgue points of \(d\)-dimensional Fourier transforms

Cites Work

• A generalization for Fourier transforms of a theorem due to Marcinkiewicz
• Christoffel functions and Fourier series for multivariate orthogonal polynomials
• On multivariate projection operators
• Triangular summability of two-dimensional Fourier transforms
• The Segal algebra \(\mathbf S_0(\mathbb R^d)\) and norm summability of Fourier series and Fourier transforms
• On convergence and growth of partial sums of Fourier series
• Wiener amalgams, Hardy spaces and summability of Fourier series
• l-1 summability of multiple Fourier integrals and positivity
• Summability of Multi-Dimensional Fourier Series and Hardy Spaces
• Wiener amalgams and pointwise summability of Fourier transforms and Fourier series
• On the convergence of multiple Fourier series
• On \(\ell-1\) Riesz summability of the inverse Fourier integral
• On uniform convergence of sequences of certain linear operators
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