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Advances in Operator Theory
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Volume Volume 4 (2019)
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Weisz, F. (2019). $\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms. Advances in Operator Theory, 4(1), 284-304. doi: 10.15352/aot.1802-1319
Ferenc Weisz. "$\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms". Advances in Operator Theory, 4, 1, 2019, 284-304. doi: 10.15352/aot.1802-1319
Weisz, F. (2019). '$\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms', Advances in Operator Theory, 4(1), pp. 284-304. doi: 10.15352/aot.1802-1319
Weisz, F. $\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms. Advances in Operator Theory, 2019; 4(1): 284-304. doi: 10.15352/aot.1802-1319

$\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms

Article 14, Volume 4, Issue 1 - Serial Number 11, Winter 2019, Page 284-304  XML PDF (134.55 K)
Document Type: Special issue: Trends in Operators on Banach Spaces
DOI: 10.15352/aot.1802-1319
Author
Ferenc Weisz email
Eotvos University, ‎Hungary
Receive Date: 21 February 2018,  Revise Date: 05 September 2018,  Accept Date: 10 September 2018 
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 Vall'ee-Poussin‎, ‎Rogosinski and Riesz summations‎.
Keywords
Fourier transforms; $ell_1$-summability; Fejér summability; $theta$-summability; Lebesgue points
Main Subjects
41. Approximations and expansions; 42. Harmonic analysis on Euclidean spaces
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