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 𝐻𝜔 𝑝,∞ on space of homogeneous type satisfying some reverse doubling condition. More precisely, we will give atomic decomposition characterizations of 𝐻𝜔 𝑝,∞ . Then we use this decomposition to derive the boundedness of fractional integral operators in 𝐻𝜔 𝑝,∞ and prove an 𝐻𝜔 𝑝,∞ interpolation theorem. As an applications, the boundedness of Nagel-Stein’s singular and fractional integral operators in 𝐻𝜔 𝑝,∞ are derived.