Our goal of this article is to introduce a new product operator that will be called $ {D^n_u} S_{\phi} $ the product of weighted differentiation and superposition operators from $ {H}^{\infty} $ to Zygmund spaces. Moreover, we characterize a necessary and sufficient conditions for $ {D^n_u} S_{\phi} $ operators from $ {H}^{\infty} $ to Zygmund spaces to be bounded and compact.
Citation: A. Kamal, M. Hamza. Eissa. A new product of weighted differentiation and superposition operators between Hardy and Zygmund Spaces[J]. AIMS Mathematics, 2021, 6(7): 7749-7765. doi: 10.3934/math.2021451
Our goal of this article is to introduce a new product operator that will be called $ {D^n_u} S_{\phi} $ the product of weighted differentiation and superposition operators from $ {H}^{\infty} $ to Zygmund spaces. Moreover, we characterize a necessary and sufficient conditions for $ {D^n_u} S_{\phi} $ operators from $ {H}^{\infty} $ to Zygmund spaces to be bounded and compact.
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A. Kamal, M. Hamza. Eissa. A new product of weighted differentiation and superposition operators between Hardy and Zygmund Spaces[J]. AIMS Mathematics, 2021, 6(7): 7749-7765. doi: 10.3934/math.2021451
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