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

Author: Yong Ding
Journal: Proc. Amer. Math. Soc. 125 (1997), 2939-2942
MSC (1991): Primary 42B20
MathSciNet review: 1401735
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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 $-1<\beta <0.$

References [Enhancements On Off] (What's this?)

  • 1. S. Chanillo, D. Watson and R. L. Wheeden, Some integral and maximal operator related to starlike sets, Studia Math. 107 (1993), 223-255. MR 94j:42027
  • 2. B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Math. Soc. 161 (1971), 249-258. MR 44:3155
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Additional Information

Yong Ding
Affiliation: Department of Mathematics, Nanchang Vocational and Technical Teacher’s College, Nanchang, Jiangxi, 330013, People’s Republic of China
Address at time of publication: No. 35, Xianshi One Road, Nanchang, Jiangxi, 330006, People’s Republic of China

Keywords: Fractional integral and maximal operators, power weights
Received by editor(s): January 24, 1996
Received by editor(s) in revised form: May 3, 1996
Additional Notes: The author was supported by NSF of Jiangxi in China
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society

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