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

Document Type: Special issue: Trends in Operators on Banach Spaces


Eotvos University, ‎Hungary


‎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.


Main Subjects