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Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces. (English) Zbl 1484.47045

Summary: We study boundedness of weighted differentiation composition operators \(D_{\varphi,u}^k\) between Zygmund type spaces \(\mathcal{Z}^\alpha\) and Bloch type spaces \(\mathcal{B}^\beta\). We also give essential norm estimates of such operators in different cases of \(k\in \mathbb{N}\) and \(0<\alpha, \beta <\infty\). Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

MSC:

47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
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