Approximation by polynomials with respect to multiplicative systems in weighted L p -spaces

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• 作者：S. S. Volosivets
• 关键词：multiplicative system ; weighted L p ; space ; K ; functional ; Jackson inequality ; Bernstein inequality ; generalized monotone sequence
• 刊名：Siberian Mathematical Journal
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：56
• 期：1
• 页码：68-77
• 全文大小：2,461 KB
• 参考文献：1. Golubov, B I, Efimov, A V, Skvortsov, V A (1987) Walsh Series and Transforms. The Theory and Applications. Nauka, Moscow
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260

文摘

We study best approximations of polynomials with respect to multiplicative systems in the L p -spaces with Muckenhoupt weights. Using Jackson’s and Bernstein’s inequalities, we obtain the direct and inverse approximation theorems in terms of the K-functional and the inverse theorem of the Timan-Besov type. In the case of a power weight, we give a criterion for the membership of a function in the weighted L p -space in terms of the Fourier coefficients with respect to multiplicative systems.