Littlewood-Paley theory and the \(T(1)\) theorem with non-doubling measures (Q5957498)

Let \(\mu\) be a Radon measure in \(\mathbb{R}^{d}\) which may be non-doubling, but should satisfy the growth condition, \(\mu(B(x,r))\leq Cr^{n}\) for all \(r\) and \(x\) and some fixed \(n\leq d\). The author develops a Littlewood-Paley theory for functions in \(L^{p}(\mu)\). Moreover, using the Littlewood-Paley decomposition for functions in \(L^{2}(\mu)\) the \(T(1)\) theorem is shown for \(n\)-dimensional Calderón-Zygmund operators, without doubling assumptions.