Fractional integrals on spaces of homogeneous type |
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Authors: | Pan Wenjie |
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Institution: | 1. Department of Mathematics, Peking University, 100871, Beijing, PRC
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Abstract: | We study fractional integrals on spaces of homogeneous type defined byI α f(x)=∫Xf(y)|B(x,d(x,y))|ga?1dμ(y), 0<α<1. If \(1< p\frac{1}{\alpha },\frac{1}{q} = \frac{1}{p} - \alpha \) , we show that Iαf is of strong type (p,q) and is of weak type ( \(\left( {1,\frac{1}{{1 - \alpha }}} \right)\) ). We also consider the necessary and sufficient conditions on two weights for which Iαf is of weak type (p,q) with respect to (w,v). |
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