Advances in Operator Theory

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

Ferenc Weisz

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‎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.

Article information

Adv. Oper. Theory, Volume 4, Number 1 (2019), 284-304.

Received: 21 February 2018
Accepted: 10 September 2018
First available in Project Euclid: 29 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B08: Summability
Secondary: 42A38‎ ‎42A24‎ ‎42B25

Fourier transforms ‎$\ell_1$-summability‎‎ Fejér summability $\theta$-summability ‎Lebesgue points


Weisz, Ferenc. $\ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms. Adv. Oper. Theory 4 (2019), no. 1, 284--304. doi:10.15352/aot.1802-1319.

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