Spaces of bounded \(\lambda\)-central mean oscillation, Morrey spaces, and \(\lambda\)-central Carleson measures
We prove that the Morrey space is contained in the space \(\text{CMO}^q\) of functions with bounded central mean oscillation, explaining in this way the dependence of \(\text{CMO}^q\) on \(q\). We also define a natural extension of \(\text{CMO}^2\), to prove the existence of a continuous bijection with central Carleson measures of order \(\lambda\). This connection is further studied to extend and refine duality results involving tent spaces and Hardy spaces associated with Herz-type spaces. Finally, we prove continuity results on these spaces for general non-convolution singular integral operators, including pseudo-differential operators with symbols in the Hörmander class \(S^m_{\rho/\delta}\), \(\rho< 1\), and linear commutators.
non-convolution singular integral operators
scientific article; zbMATH DE number 1454850