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
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.
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