Estimates of essential norms of weighted composition operator from Bloch type spaces to Zygmund type spaces

2013/12/30 by Liang, Yu-Xia, Zhou, Ze-Hua
#26A24 #30H30 #47B33 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1401.0031

Abstract

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk \mathbbD in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uC_φ from Bloch type spaces to Zygmund type spaces in \mathbbD in terms of u, φ, their derivatives and the n-th power φⁿ of φ. Moreover, we obtain some similar estimates for their essential norms. From which the sufficient and necessary conditions of compactness of the operators uC_φ follows immediately.

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