Abstract:
A necessary and sufficient condition of absolute |C;¯β|λ-summability almost everywhere on Ts is obtained for multiple trigonometric Fourier series of functions f∈L¯q(Ts) from generalized Besov classes Bωr¯q,s,θ, where Ts=[0,2π)s, ¯β=(β1,β2,…,βs), ¯q=(q1,q2,…,qs), 1<qj⩽2, ¯1,s, 1⩽λ⩽qs⩽…⩽q1, λ<θ<∞, 0⩽βj<1/q′j=1−1/qj, ¯1,s, r∈N, r>∑sj=1(1/qj−βj), and ωr is a function of the type of modulus of smoothness of order r.
\Bibitem{Bit19}
\by S.~Bitimkhan
\paper Conditions of absolute cesaro summability of multiple trigonometric Fourier series
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 2
\pages 42--47
\mathnet{http://mi.mathnet.ru/timm1622}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-2-42-47}
\elib{https://elibrary.ru/item.asp?id=38071598}
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https://www.mathnet.ru/eng/timm1622
https://www.mathnet.ru/eng/timm/v25/i2/p42
This publication is cited in the following 1 articles:
S. Bitimkhan, D. T. Alibieva, “Partial best approximations and the absolute Cesaro summability of multiple Fourier series”, Bull. Karaganda Univ-Math., 103:3 (2021), 4–12