The Weighted L1-integrability of functions and the parseval equality with respect to multiplicative systems

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• 作者：S. S. Volosivets (1) VolosivetsSS@mail.ru
• 关键词：and phrases multiplicative systems of bounded type – ; weighted L1 ; integrability – ; generalized monotonicity
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：56
• 期：8
• 页码：11-21
• 全文大小：547.2 KB
• 参考文献：1. V. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Walsh Series and Transforms (Nauka, Moscow, 1987) [in Russian].
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  6. R. P. Boas, Integrability Theorems for Trigonometric Transforms (Springer, N.Y., 1967).
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  9. S. S. Volosivets, “Certain Conditions in the Theory of Series with Respect toMultiplicative Systems,” Anal. Math. 33(3), 227–246 (2007).
  10. G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli, and A. I. Rubinshtein, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups (Elm, Baku, 1981) [in Russian].
  11. J. A. Gosselin, “Convergence A. E. of Vilenkin-Fourier Series,” Trans. Amer. Math. Soc. 185, 345–370 (1973).
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• 作者单位：1. Saratov State University, ul. Astrakhanskya 83, Saratov, 410012 Russia
• ISSN：1934-810X

文摘

In this paper we prove necessary and sufficient conditions for the weighted L 1-integrability of functions defined on [0, 1) in terms of Fourier coefficients with respect to a multiplicative system of bounded type. These results are counterparts of trigonometric ones obtained by M. and S. Izumi and M. M. Robertson.