Triangular summability and Lebesgue points of $2$ -dimensional Fourier transforms

Abstract

We consider the triangular θ-summability of 2-dimensional Fourier transforms. Under some conditions on θ, we show that the triangular θ-means of a function f belonging to the Wiener amalgam space W(L1,ℓ∞)(R2) converge to f at each modified strong Lebesgue point. The same holds for a weaker version of Lebesgue points for the so-called modified Lebesgue points of f∈W(Lp,ℓ∞)(R2) whenever 1<p<∞. Some special cases of the θ-summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.