Revistes Catalanes amb Accés Obert (RACO)

Spaces of bounded $\lambda$-central mean oscillation, Morrey spaces, and $\lambda$-central Carleson measures

Joseph D. Lakey, Martha Guzmán-Partida, Josefina D. Álvarez Alonso


We prove that the Morrey space is contained in the space $CMO^q$ of functions with bounded central mean oscillation, explaining in this way the dependence of $ CMO^q$ on $q$. We also define a natural extension of $CMO^2$, 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.

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