WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES

doi:10.1016/S0252-9602(11)60264-6

Abstract

Abstract:

In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are ifferent counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.

Key words: Vector-valued analytic unction, Dirichlet space, weighted composition operator, boundedness

CLC Number:

47B33

WANG Mao-Fa. WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES[J].Acta mathematica scientia,Series B, 2011, 31(2): 641-651.

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