Weighted Norm Inequalities for Convolutions, Differential Operators, and Generalized Hypergeometric Functions

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• 作者：Arcadii Z. Grinshpan (1)
  
• 关键词：26D10 ; 26D15 ; 30B10 ; 44A35 ; 33B15 ; 44A10 ; 45D05 ; Convolutions ; Volterra integral equations ; seminorms for formal power series ; weighted inequalities for sums and integrals ; integro ; differential inequalities ; linear differential operators ; generalized hypergeometric series ; confluent hypergeometric functions ; Laplace鈥揃orel transforms
• 刊名：Integral Equations and Operator Theory
• 出版年：2013
• 出版时间：February 2013
• 年：2013
• 卷：75
• 期：2
• 页码：165-185
• 全文大小：327KB
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• 作者单位：Arcadii Z. Grinshpan (1)
  
  1. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA
  
• ISSN：1420-8989

文摘

The recent work on discrete inequalities with the binomially made weights leads to a sharp weighted norm inequality for convolutions of complex-valued functions on a finite interval. This result and the Hadamard-type modifications of power series provide the basis for an integral approach to solution-kernel estimates for Volterra convolution equations and for various integro-differential and special function applications. The development of this approach and the new weighted norm inequalities for linear differential operators and generalized hypergeometric functions are presented in this paper.