Singular integral operators bounded on Orlicz spaces and Orlicz type Hardy spaces (The generalization of function spaces and its enviroment)

Abstract

We study the singular integral operators which have standard kernels and which are bounded on Orlicz spaces. We generalize the T1 theorem on Orlicz spaces and investigate Their boundedness from the Orlicz type Hardy space H1Φ to L1 and from L∞ to the Orlicz type BMO (namely BMOΦ). Furthermore, we prove that these operators can be extended to bounded operators on some homogenous Sovolev spaces.