THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

doi:10.1007/s10473-021-0512-7

Abstract

Abstract: There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions. In this paper, we present an equivalent characterization for the boundedness of the product operator $C_\varphi D^m$ acting on Bloch-type spaces of slice regular functions. After that, an equivalent estimation for its essential norm is established, which can imply several existing results on holomorphic spaces.

Key words: essential norm, differentiation, composition operator, Bloch-type space, slice regular functions

CLC Number:

30D45

Yuxia LIANG. THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS[J].Acta mathematica scientia,Series B, 2021, 41(5): 1606-1618.

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