Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

Abstract

We prove the strong-type and weak-type estimates for the Calderón–Zygmund singular integrals on central Morrey–Orlicz and weak central Morrey–Orlicz spaces defined in our earlier paper [26]. Next part has similar investigations between distinct central Morrey–Orlicz and weak central Morrey–Orlicz spaces. Then we define the $\lambda$-central mean oscillation–Orlicz spaces and its weak version investigating also some estimates for a modified Calderón–Zygmund singular integrals. Also, we show boundedness of a modified Calderón–Zygmund singular integrals from central Morrey–Orlicz spaces to $\lambda$-central mean oscillation–Orlicz spaces, even for different Orlicz functions, and corresponding weak version.