GENERALIZED COMPOSITION OPERATORS ON ZYGMUND SPACES AND BLOCH TYPE SPACES

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The boundedness and compactness of the generalized composition operator on Zygmund spaces and Bloch type spaces are investigated in this paper.

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Products of composition and differentiation operators on the weighted Bergman space (2009, background): “Products of integral, differentiation and composition operators on spaces of analytic functions are studied in [4, 5, 11, 12, 13, 14, 16, 19, 29, 31, 34, 35].”
Integral-type operators from a mixed norm space to a bloch-type space on the unit ball (2009, background): “Motivated by the fact that composition operators and weighted composition operators naturally come from isometries of some function spaces (see [7]), S. Li and the author introduced the generalized composition operator on H(D) in [ 8 ] as follows:”
On an integral operator between Bloch-type spaces on the unit ball (2010, background): “One of motivations for introducing operator I φ stems from the operator introduced in [17].”
Products of integral-type operators and composition operators between Bloch-type spaces (2009, background): “Some related operators can be also found in [6,19,27,28].”