Weighted norm inequalities for potential operators
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- Trans. Amer. Math. Soc. 308 (1988), 57-68 Request permission
Abstract:
We give sufficient conditions for inequalities of the form \[ {\left ( {\int {{{\left ( {\int {G(x - y)f(y) d\mu (y)} } \right )}^q} d\omega (x)} } \right )^{1/q}} \leqslant C{\left ( {\int {|f(y){|^p}d\nu (y)} } \right )^{1/p}}\] to hold for measurable functions $f$. We determine the dependence of the constant $C$ on the measures $\mu$, $\nu$, $\omega$ and give some applications.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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