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

Ferenc Weisz | Zendy

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

Author(s) -

Ferenc Weisz

Publication year - 2018

Publication title -

advances in operator theory

Language(s) - English

Resource type - Journals

eISSN - 2662-2009

pISSN - 2538-225X

DOI - 10.15352/aot.1802-1319

Subject(s) - mathematics , lebesgue integration , almost everywhere , pure mathematics , hardy space , standard probability space , bessel function , space (punctuation) , lp space , function (biology) , mathematical analysis , banach space , philosophy , linguistics , evolutionary biology , biology

The classical Lebesgue’s theorem is generalized, and it is proved that under some conditions on the summability function θ, the l1-θ-means of a function f from the Wiener amalgam space W (L1, l∞)(R) ⊃ L1(R) converge to f at each modified strong Lebesgue point and thus almost everywhere. The θ-summability contains the Weierstrass, Abel, Picard, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.

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