Open AccessHardy operator with variable limits on monotone functions
Author(s) -
V. D. Stepanov,
E. P. Ushakova
Publication year - 2003
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2003/860547
Subject(s) - mathematics , monotone polygon , operator (biology) , variable (mathematics) , pure mathematics , mathematical analysis , biochemistry , chemistry , geometry , repressor , transcription factor , gene
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
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