On maximal rearrangement inequalities for the Fourier transform
W. B. Jurkat,G. Sampson +1 more
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This article is published in Transactions of the American Mathematical Society.The article was published on 1984-02-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Discrete Fourier transform (general) & Fourier transform on finite groups.read more
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On rearrangement and weight inequalities for the Fourier transform
W. B. Jurkat,G. Sampson +1 more
TL;DR: On considere la transformee de Fourier a n dimensions (n≥1) f(x)=∫ R nf(y)e(x.y) dy, e(t)=exp(2πit) pour t∈R, ou x.y est le produit scalaire et f∈L 1 (R n ) ou L 2 (R N ) oui L 2(R n) ou juste une fonction test.
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Vector-valued Hausdorff-Young inequality and applications
TL;DR: The Fourier type of Banach spaces with respect to groups has been studied in this paper, where the Rademacher type and cotype of the Fourier transform of smooth functions have been compared to general orthonormal systems.
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Hardy integral estimates for the Laplace transform
TL;DR: Weighted norm inequalities for the Laplace transform are obtained by reducing LP estimates to the Hardy antidifferentiation operator as discussed by the authors, which yields a fairly sharp weighted norm inequality for LP estimates.
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Weighted norm inequalities for integral transforms
TL;DR: In this paper, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates for the cosine and sine Fourier transforms.
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Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
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