Two-Weight Inequality of Calderón-Zygmund Operator on Non-Homogeneous Metric Measure Space (Analysis in Theory and Applications, 2025)
Let $(\mathcal{X}, d, μ)$ 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 Calderón-Zygmund operator on $(\mathcal{X}, d, μ)$. 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 Calderón-Zygmund operators on the non-homogeneous metric measure spaces which is interesting in its own right.