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Weak type bounds for a class of rough operators with power weights

Authors:	Yong Ding

Institution:	Department of Mathematics, Nanchang Vocational and Technical Teacher's College, Nanchang, Jiangxi, 330013, People's Republic of China

Abstract:	In this note we show that $T_{\Omega ,\alpha }$ and $M_{\Omega ,\alpha },$ the fractional integral and maximal operators with rough kernel respectively, are bounded operators from $L^{1}(\|x\|^{\beta (n-\alpha )/n},\mathbb {R}^{n})$ to $L^{n/(n-\alpha ),\infty }(\|x\|^{\beta },\mathbb {R}^{n}),$ where $0<\alpha <n$ and $-1<\beta <0.$

Keywords:	Fractional integral and maximal operators power weights

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