Weighted Integrability of Double Series with Respect to Multiplicative Systems

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• 作者：S. S. Volosivets ; R. N. Fadeev
• 刊名：Journal of Mathematical Sciences
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：209
• 期：1
• 页码：51-65
• 全文大小：211 KB
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• 作者单位：S. S. Volosivets (1)
  R. N. Fadeev (1)
  
  1. Saratov State University, Saratov, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8795

文摘

Necessary and sufficient conditions for L p -integrability with power weight of a function f represented by the double series with respect to a multiplicative system with generalized monotone coefficients are obtained. These conditions are given in terms of the coefficients or their second mixed differences. In addition, the integrability of the difference quotient (f(x, y) ?f(x, 0) ?f(0, y) + f(0, 0))/(xy) is studied.