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Hardy operator with variable limits on monotone functions

By Vladimir D. Stepanov and Elena P. Ushakova


We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits

Topics: Mathematics, QA1-939
Publisher: Hindawi Publishing Corporation
Year: 2003
DOI identifier: 10.1155/2003
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