Another proof of the boundedness of Calderón–Zygmund singular integrals on generalized Orlicz spaces

Abstract

We use the atomic decomposition of the generalized Orlicz–Hardy space to reprove that Calderón–Zygmund singular integrals are bounded on the generalized Orlicz space, which was obtained in [7, Corollary 6.2] where the authors applied extrapolation on the generalized Orlicz space to prove it. By our method, we assume a weaker regularity on the kernel of Calderón–Zygmund singular integral operators.