“…The problems of approximation theory in weighted and nonweighted Lebesgue spaces, weighted and nonweighted Orlicz spaces have been investigated by several authors (see, e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][30][31][32]36,37,45,46]). …”
Section: Theorem 16 [20] If Is a Dini-smooth Curvementioning
We investigate problems of estimating the deviation of functions from their de la Vallée-Poussin sums in weighted Orlicz spaces L M (T, ω) in terms of the best approximation
“…The problems of approximation theory in weighted and nonweighted Lebesgue spaces, weighted and nonweighted Orlicz spaces have been investigated by several authors (see, e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][30][31][32]36,37,45,46]). …”
Section: Theorem 16 [20] If Is a Dini-smooth Curvementioning
We investigate problems of estimating the deviation of functions from their de la Vallée-Poussin sums in weighted Orlicz spaces L M (T, ω) in terms of the best approximation
“…Approximation by trigonometric polynomials and other related problems in the Orlicz and weighted Orlicz spaces were studied in [2,[8][9][10][11][12]17,18,21,23,24].…”
Abstract. In the present work we prove some direct theorems of the approximation theory in the weighted Orlicz spaces with weights satisfying so called Muckenhoupt's condition and we obtain some estimates for the deviation of a function in the weighted Orlicz spaces from the linear operators constructed on the basis of its Fourier series.
“…For example, the problems of approximation theory for Smirnov classes with variable exponent, weighted Smirnov classes, weighted Smirnov Orlicz classes and weighted rearrangement invariant Smirnov classes were studied in [4][5][6][7][8]. But the approximation problems in the doubly connected domains were not investigated sufficiently wide.…”
Section: Is the N Th Partial Sum Of The Taylor Series Of G At The Orimentioning
In this article, we investigate the direct problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on a doubly connected domain bounded by two Dini-smooth curves.
Mathematics Subject Classification
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