Boundedness and Compactness of Composition Operators on Variable Exponent Bergman Spaces

Atomic Decomposition and Composition Operators on Variable Exponent Bergman Spaces

“…It's well known that the composition operator C ϕ is bounded on classical Hardy, Bergman and Bloch spaces on D. In [13], the authors proved that C ϕ is necessarily bounded on variable exponent Bergman spaces A p(•) (D) when p(•) ∈ P log (D). However, we point out that there is a mistake in their proof.…”