“…More general doubling weights, approximation by trigonometric polynomials in the periodic case and other related problems were studied in [29], [30], [31], [7]. Direct and converse results in the case of exponential weights on the real line were obtained in [14] and [15].…”
Section: From the Hölder Inequality It Follows That Ifmentioning
Abstract. We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.
“…More general doubling weights, approximation by trigonometric polynomials in the periodic case and other related problems were studied in [29], [30], [31], [7]. Direct and converse results in the case of exponential weights on the real line were obtained in [14] and [15].…”
Section: From the Hölder Inequality It Follows That Ifmentioning
Abstract. We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.
“…For the more general doubling weights, approximation by trigonometric polynomials in the periodic case and other related problems were studied in [4,[29][30][31]. The direct and converse results in case of the exponential weights given on the real line were obtained in [13,14].…”
Section: Introduction and The Main Resultsmentioning
Abstract. We investigate the approximation properties of trigonometric polynomials and prove some direct and inverse theorems for polynomial approximation in weighted rearrangement invariant spaces.
“…For more general doubling weights, approximation by trigonometric polynomials and other related problems in the weighted Lebesgue spaces were studied in [2], [20], [19] and [21]. Some interesting results concerning best polynomial approximation in weighted Lebesgue spaces were also proved in [4] and [6].…”
Section: If ω ∈ a P(m ) Then It Can Be Easily Seen That L Mω (T) ⊂mentioning
ABSTRACT. We prove some direct and converse theorems of trigonometric approximation in weighted Orlicz spaces with weights satisfying so called Muckenhoupt's A p condition.
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