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January 2017 Triangular summability and Lebesgue points of 2-dimensional Fourier transforms
Ferenc Weisz
Banach J. Math. Anal. 11(1): 223-238 (January 2017). DOI: 10.1215/17358787-3796829


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.


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Ferenc Weisz. "Triangular summability and Lebesgue points of 2-dimensional Fourier transforms." Banach J. Math. Anal. 11 (1) 223 - 238, January 2017.


Received: 26 January 2016; Accepted: 24 March 2016; Published: January 2017
First available in Project Euclid: 9 December 2016

zbMATH: 1354.42013
MathSciNet: MR3582397
Digital Object Identifier: 10.1215/17358787-3796829

Primary: 42B08
Secondary: 42A24 , 42A38 , 42B25

Keywords: $\theta$-summability , Fejér summability , Fourier transforms , ‎Lebesgue points , triangular summability

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 1 • January 2017
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