(untitled) (Analysis in Theory and Applications, 2025)
Let (X, d, μ) be a non-homogeneous metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, we study weighted inequalities of the Calder\’on-Zygmund operator on (X, d, μ). Specifically, for 1 < p < ∞, we identify sufficient conditions for the weight on one side, which guarantee the existence of another weight in the other side, so that the weighted L^p inequality holds. We deal with this problem by developing a vector-valued theory for Calder\’on-Zygmund operators on the non-homogeneous metric measure spaces which is interesting in its own right.