New characterizations for differences of weighted differentiation composition operators from a Bloch-type space to a weighted-type space

Abstract

We found several new equivalent characterizations for the boundedness of the differences of weighted differentiation composition operators from Bloch-type space to weighted-type space. Especially, we estimated its essential norm in terms of the n-th power of the induced analytic self-maps on the unit disk, which can provide a new and simple compactness criterion.2010 Mathematics Subject Classification. Primary 47B38; Secondary 30H30, 47B33.

Estimates on Some General Classes of Holomorphic Function Spaces

“…Composition operators on weighted classes of function spaces are intensively researched by several authors (see [4,5,[14][15][16][17][18][19] and others). Nevanlinna-type counting functions are playing a significant role in such studies.…”

Differences of composition operators from Zygmund-type spaces to Bloch-type spaces

“…So many researchers turned to carry out extensive research on the difference of composition operator C ϕ − C ψ acting on various holomorphic spaces. The related research could be referred into [1,5,6,10,14,16,18,23,25], especially [8,13,22].…”