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

Abstract

Listen

Translate article

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.