Banach Journal of Mathematical Analysis

Triangular summability and Lebesgue points of 2-dimensional Fourier transforms

Ferenc Weisz

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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,)(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 fW(Lp,)(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.

Article information

Banach J. Math. Anal. Volume 11, Number 1 (2017), 223-238.

Received: 26 January 2016
Accepted: 24 March 2016
First available in Project Euclid: 9 December 2016

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Zentralblatt MATH identifier

Primary: 42B08: Summability
Secondary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42A24: Summability and absolute summability of Fourier and trigonometric series 42B25: Maximal functions, Littlewood-Paley theory

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


Weisz, Ferenc. Triangular summability and Lebesgue points of $2$ -dimensional Fourier transforms. Banach J. Math. Anal. 11 (2017), no. 1, 223--238. doi:10.1215/17358787-3796829.

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