Article
Weighted norm inequalities for singular integral operators
Author/s | Pérez Moreno, Carlos |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 1994-04 |
Deposit Date | 2016-10-10 |
Published in |
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Abstract | For a Calderón-Zygmund singular integral operator T, we show that the following weighted inequality holds Z Rn|T f(y)|p w(y)dy ≤ C Z Rn |f(y)|
p M[p]+1w(y)dy, where Mk is the Hardy-Littlewood maximal operator M iterated ... For a Calderón-Zygmund singular integral operator T, we show that the following weighted inequality holds Z Rn|T f(y)|p w(y)dy ≤ C Z Rn |f(y)| p M[p]+1w(y)dy, where Mk is the Hardy-Littlewood maximal operator M iterated k times, and [p] is the integer part of p. Moreover, the result is sharp since it does not hold for M[p]. We also give the following endpoint result: w({y ∈ R n : |T f(y)| > λ}) ≤ C λ Z Rn |f(y)| M2w(y)dy. |
Citation | Pérez Moreno, C. (1994). Weighted norm inequalities for singular integral operators. Journal of the London Mathematical Society, 49 (2), 296-308. |
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