Net Spaces and Boundedness of Integral Operators |
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| Authors: | Erlan Nursultanov Sergey Tikhonov |
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| Affiliation: | 1.Gumilyov Eurasian National University,Astana,Kazakhstan;2.ICREA and Centre de Recerca Matemàtica,Campus de Bellaterra, Edifici C,Bellaterra (Barcelona),Spain |
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| Abstract: | In this paper we introduce new functional spaces which we call net spaces. Using their properties, necessary and sufficient conditions for the integral operators to be of strong or weak type are obtained. Estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented. |
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