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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weighted norm inequalities for potential operators


Author: Martin Schechter
Journal: Trans. Amer. Math. Soc. 308 (1988), 57-68
MSC: Primary 26D10; Secondary 42B25, 47A30
DOI: https://doi.org/10.1090/S0002-9947-1988-0946429-3
MathSciNet review: 946429
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Abstract: We give sufficient conditions for inequalities of the form

$\displaystyle {\left( {\int {{{\left( {\int {G(x - y)f(y)\,d\mu (y)} } \right)}... ...1/q}}\, \leqslant C{\left( {\int {\vert f(y){\vert^p}d\nu (y)} } \right)^{1/p}}$

to hold for measurable functions $ f$. We determine the dependence of the constant $ C$ on the measures $ \mu $, $ \nu $, $ \omega $ and give some applications.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0946429-3
Keywords: Weighted norm inequalities, potential operators, maximal operators
Article copyright: © Copyright 1988 American Mathematical Society