On the exponential integrability of fractional integrals on spaces of homogeneous type

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Authors ¹, ¹

Department of Mathematical Sciences, DePaul University, 2219 North Kenmore Ave., Chicago, Illinois 60614, U.S.A.

In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds

L^{\frac{1}{α}}

into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].

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