Geodesic
Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel
Canadian journal of mathematics, Tome 50 (1998) no. 1, pp. 29-39

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Given function $\Omega $ on ${{\mathbb{R}}^{n}}$ , we define the fractional maximal operator and the fractional integral operator by $${{M}_{\Omega ,\,\alpha }}f(x)\,=\,_{r>0}^{\sup }\frac{1}{{{r}^{n-\alpha }}}\,\int{{{_{|y|}}_{<r}}\,}|\Omega (y)|\,|f(x-y)|\,dy$$ and $${{T}_{\Omega ,\,\alpha }}f(x)\,=\,\int{_{{{\mathbb{R}}^{n}}}}\,\frac{\Omega (y)}{{{\left| y \right|}^{n-\alpha }}}f(x-y)dy$$ respectively, where $0\,<\,\alpha \,<\,n$ . In this paper we study the weighted norm inequalities of ${{M}_{\Omega ,\,\alpha }}$ and ${{T}_{\Omega ,\,\alpha }}$ for appropriate $\alpha ,\,s$ and $A(p,\,\,q)$ weights in the case that $\Omega \,\in \,{{L}^{s}}({{S}^{n-1}})(s>1)$ , homogeneous of degree zero.
DOI : 10.4153/CJM-1998-003-1
Mots-clés : 42B20, 42B25 
Ding, Yong; Lu, Shanzhen. Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel. Canadian journal of mathematics, Tome 50 (1998) no. 1, pp. 29-39. doi: 10.4153/CJM-1998-003-1
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1998-003-1/}
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