Hiroshima Mathematical Journal

A weighted weak type estimate for the fractional integral operator on spaces of homogeneous type

Qihui Zhang

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Abstract

Let $(\mathscr{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we give a sufficient condition on the pair of weights $(u,\,v)$ so that the fractional integral operator on spaces of homogeneous type is bounded from $L^p(\mathscr{X},\,v)$ to weak $L^q(\mathscr{X},\,u)$ with $1<p\leq q<\infty$.

Article information

Source
Hiroshima Math. J., Volume 41, Number 3 (2011), 389-407.

Dates
First available in Project Euclid: 12 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1323700041

Digital Object Identifier
doi:10.32917/hmj/1323700041

Mathematical Reviews number (MathSciNet)
MR2895287

Zentralblatt MATH identifier
1235.42011

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Keywords
Spaces of homogeneous type weighted norm inequality fractional integral operator

Citation

Zhang, Qihui. A weighted weak type estimate for the fractional integral operator on spaces of homogeneous type. Hiroshima Math. J. 41 (2011), no. 3, 389--407. doi:10.32917/hmj/1323700041. https://projecteuclid.org/euclid.hmj/1323700041


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