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On the mean summability by Cesaro method of fourier trigonometric series in two-weighted setting.
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The Cesaro summability of trigonometric Fourier series is investigated in the weighted Lebesgue spaces in a two-weight case, for one and two dimensions. These results are applied to the prove of two-weighted Bernstein's inequalities for trigonometric polynomials of one and two variables.
1. Introduction
It is well known that (see [9]) Cesaro means of 2[pi]-periodic functions f [member of] [L.sup.P]([??]) (1 [less than or equal to] p [less than or equal to] [infinity]) converges by norms. Hereby [??] is denoted the interval (-[pi], [pi]). The problem of the ...
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