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Winter 2019 $\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms
Ferenc Weisz
Adv. Oper. Theory 4(1): 284-304 (Winter 2019). DOI: 10.15352/aot.1802-1319

Abstract

‎The classical Lebesgue's theorem is generalized‎, ‎and it is proved that under some conditions on the summability function $\theta$‎, ‎the $\ell_1$-$\theta$-means of a function $f$ from the Wiener amalgam space $W(L_1,\ell_\infty)(\R^d)\supset L_1(\R^d)$ converge to $f$ at each modified strong Lebesgue point and thus almost everywhere‎. ‎The $\theta$-summability contains the Weierstrass‎, ‎Abel‎, ‎Picard‎, ‎Bessel‎, Fejér‎, ‎de La Vallée-Poussin‎, ‎Rogosinski‎, ‎and Riesz summations‎.

Citation

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Ferenc Weisz. "$\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms." Adv. Oper. Theory 4 (1) 284 - 304, Winter 2019. https://doi.org/10.15352/aot.1802-1319

Information

Received: 21 February 2018; Accepted: 10 September 2018; Published: Winter 2019
First available in Project Euclid: 29 September 2018

zbMATH: 06946455
MathSciNet: MR3862622
Digital Object Identifier: 10.15352/aot.1802-1319

Subjects:
Primary: 42B08
Secondary: 42A24, 42A38, 42B25

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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