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 Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 2, Pages 42–47 (Mi timm1622)

Conditions of absolute cesaro summability of multiple trigonometric Fourier series

S. Bitimkhan

E. A. Buketov Karaganda State University

Abstract: A necessary and sufficient condition of absolute $|C;\overline{\beta}|_\lambda$-summability almost everywhere on ${\mathbb T}^s$ is obtained for multiple trigonometric Fourier series of functions $f\in L_{\overline{q}}({\mathbb T}^s)$ from generalized Besov classes $B_{\overline q,s,\theta}^{\omega_r}$, where ${\mathbb T}^s=[0,2\pi)^s$, $\overline{\beta}=(\beta_1,\beta_2,\ldots,\beta_s)$, $\overline{q}=(q_1,q_2,\ldots, q_s)$, $1<q_j\le 2$, $\overline{1,s}$, $1\le \lambda\le q_s\le \ldots\le q_1$, $\lambda<\theta<\infty$, $0\le \beta_j<1/q'_j=1-1/q_j$, $\overline{1,s}$, $r\in \mathbb{N}$, $r>\sum_{j=1}^s(1/q_j-\beta_j)$, and $\omega_r$ is a function of the type of modulus of smoothness of order $r$.

Keywords: multiple trigonometric Fourier series, absolute summability, modulus of smoothness, generalized Besov class.

DOI: https://doi.org/10.21538/0134-4889-2019-25-2-42-47

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UDC: 517.518.476
MSC: 42A24

Citation: S. Bitimkhan, “Conditions of absolute cesaro summability of multiple trigonometric Fourier series”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 2, 2019, 42–47

Citation in format AMSBIB
\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{http://elibrary.ru/item.asp?id=38071598}