A new product of superposition and differentiation operators between Hardy and Zygmund spaces

Abstract

Our goal in this article is to  characterize the boundedness and the compactness of the product of the superposition operator followed by the differentiation operator $DS_{\phi}$ from the ${H}^{\infty}$ space to the  Zygmund space. Moreover, we give the necessary and sufficient conditions  for the $DS_{\phi}$ operator  from the  ${H}^{\infty}$  space to the Zygmund space to be bounded and compact.