$ell_1$-summability and Lebesgue points of $d$-dimensional Fourier transforms
2019
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, Fejer, de La Vallee-Poussin, Rogosinski, and Riesz summations.
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