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Abstract  

We prove a version of the Orlicz-Pettìs theorem within the frame of the Statistical Cesàro summability.

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. Bibliografia [1] Chanillo , S. and Muckenhoupt , B. , Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series , Mem. Arrier. Math. Sac. 102

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Abstract

It is proved that the maximal operator of the triangular Cesàro means of a two-dimensional Fourier series is bounded from the periodic Hardy space to for all 2/(2+α)<p≦∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Cesàro means of a function converge a.e. to f.

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Abstract  

We prove the following theorem. Assume fL (R 2) with bounded support. If f is continuous at some point (x 1,x 2) ∈ R 2, then the double Fourier integral of f is strongly q-Cesro summable at (x 1,x 2) to the function value f(x 1,x 2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
of R 2, then the strong q-Cesro summability of the double Fourier integral of f is locally uniform on
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{G}$$ \end{document}
.

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Изучается суммирова ние ортогональных последовательносте й почти всюду методам и Чезаро (C, α). В частности, доказаны два утвержд ения. Пусть 0<α<1. 1) Всякая орто-гональная последовательность (ξ k), ∥ξ k∥=a k, суммируема почти всюду методом (C, α), если . 2) Если , то существует последовательность независимых и ортогональных случа йных величин, не сумми руемая методом (C, α) почти всюд у; ∥ξ k∥= =¦a k¦.

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Abstract  

The aim of this paper is to give weighted function spaces in which the sequence of Cesàro means of the Jacobi-Fourier series are uniformly convergent. Error estimate for the approximation will also be considered.

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