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Weighted Convolution Operators on $\ell_p$

  Published:2005-06-01
 Printed: Jun 2005
  • David Borwein
  • Werner Kratz
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Abstract

The main results deal with conditions for the validity of the weighted convolution inequality $\sum_{n\in\mathbb Z}\left|b_n\sum_{k\in\mathbb Z} a_{n-k}x_k\right|^p\le C^p\sum_{k\in\mathbb Z} |x_k|^p$ when $p\ge1$.
Keywords: convolution operators on $\ell_p$ convolution operators on $\ell_p$
MSC Classifications: 40G10;, 40E05 show english descriptions unknown classification 40G10;
Tauberian theorems, general
40G10; - unknown classification 40G10;
40E05 - Tauberian theorems, general
 

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