Difference of Composition Operators on Weighted Bergman Spaces with Doubling Weights

Difference of composition-differentiation operators from Hardy spaces to weighted Bergman spaces via harmonic analysis

“…Although the converse inequality does not hold we have the following result, which can be found in [9, Theorem 2.8] or [26,Lemma D]. Since Koo and Wang's result is stated for the unit ball setting (see [9]), for the convenience of readers, and in order to offer no doubt of the validity of the result, we give a proof here.…”

“…authors on several function spaces. See [7,9,10,12,[24][25][26] for example. In 2004, Nieminen and Saksman [16] showed that the compactness of C ϕ − C ψ on H p , with 1 ≤ p < ∞, is independent of p. Very recently, in [2], Choe et al completely characterized compact operators C ϕ − C ψ on H p by using Carleson measures of Bergman spaces.…”