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Weighted Convolution Operators on ℓp
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- Journal:
- Canadian Mathematical Bulletin / Volume 48 / Issue 2 / 01 June 2005
- Published online by Cambridge University Press:
- 20 November 2018, pp. 175-179
- Print publication:
- 01 June 2005
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- Article
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The main results deal with conditions for the validity of the weighted convolution inequality
${{\sum }_{n\in \mathbb{Z}}}|{{b}_{n}}\,{{\sum }_{k\in \mathbb{Z}}}{{a}_{n-{{k}^{x}}k}}{{|}^{p}}\,\le \,{{C}^{p\,}}\,{{\sum }_{k\in \mathbb{Z}}}\,{{\left| {{x}_{k}} \right|}^{p}}$ when 
$p\,\ge \,1$.
