Boundedness of Fractional Integral Operators in Weighted Weak Hardy Spaces on Homogeneous Spaces

Abstract

In this paper, we shall study the theory of weighted weak Hardy spaces ð»ðœ” ð‘,∞ on space of homogeneous type satisfying some reverse doubling condition. More precisely, we will give atomic decomposition characterizations of ð»ðœ” ð‘,∞ . Then we use this decomposition to derive the boundedness of fractional integral operators in ð»ðœ” ð‘,∞ and prove an ð»ðœ” ð‘,∞ interpolation theorem. As an applications, the boundedness of Nagel-Stein’s singular and fractional integral operators in ð»ðœ” ð‘,∞ are derived.