On weighted inequalities for singular integrals期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On weighted inequalities for singular integrals

Authors:	H Aimar L Forzani F J Martí n-Reyes

Institution:	Dept. Matematica, FIQ, Prop.CAI+D, INTEC, Gëmes 3450, 3000 Santa Fe, Argentina ; Dept. Matematica, FIQ, Prop.CAI+D, INTEC, Gëmes 3450, 3000 Santa Fe, Argentina F. J. Martín-Reyes ; Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

Abstract:	In this note we consider singular integrals associated to Calderón-Zygmund kernels. We prove that if the kernel is supported in $(0,\infty )$ then the one-sided $A_{p}$ condition, $A_{p}^{-}$ , is a sufficient condition for the singular integral to be bounded in $L^{p}(w)$ , $1<p<\infty$ , or from $L^{1}(wdx)$ into weak- $L^{1}(wdx)$ if . This one-sided $A_{p}$ condition becomes also necessary when we require the uniform boundedness of the singular integrals associated to the dilations of a kernel which is not identically zero in $(0,\infty )$ . The two-sided version of this result is also obtained: Muckenhoupts $A_{p}$ condition is necessary for the uniform boundedness of the singular integrals associated to the dilations of a general Calderón-Zygmund kernel which is not the function zero either in $(-\infty ,0)$ or in $(0,\infty )$ .

Keywords:	Singular integrals Calderon-Zygmund operators weights

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