Calderón-Zygmund operators on Herz type Hardy spaces

We consider the boundedness of Calderón-Zygmund operators from to , where is the Hardy space associated with the Herz space and is the local version of . We show Calderón's commutator is bounded from to .     

Fractional integrals on weighted Hardy spaces

In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to .     

A note on maximality of analytic crossed products

Let G be a compact abelian group with the totally ordered dual group which admits the positive semigroup . Let N be a von Neumann algebra and be an automorphism group of on N. We denote to the analytic crossed product determined by N and α. We show that if is a maximal σ-weakly closed subalgebra of , then induces an archimedean order in .