Abstract
We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund-type spaces. Consequently, we obtain new characterizations for the compactness of such operators.
Highlights
Let D denote the open unit ball of the complex plane C and HðDÞ denote the space of all complex-valued analytic functions on D
Essential norm estimates of different types of operators between various classes of Banach spaces have been studied by many authors
Operator theoretic properties of composition operators have been studied by many authors between different classes of analytic function spaces
Summary
Let D denote the open unit ball of the complex plane C and HðDÞ denote the space of all complex-valued analytic functions on D. Essential norm estimates of different types of operators between various classes of Banach spaces have been studied by many authors (see, for example, [2,3,4,5,6,7], and references therein). Operator theoretic properties of (weighted) composition operators have been studied by many authors between different classes of analytic function spaces (see, for example, [4, 5, 8, 9], and the references therein). Boundedness and compactness of generalized weighted composition operators have been studied between Blochtype spaces and Zygmund-type spaces in [2, 12] and between. We first study boundedness of generalized weighted composition operators between Zygmund-type spaces and give new characterizations for the boundedness of these operators.
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