Generalized Weighted Composition Operators on Weighted Bergman Spaces

Weighted Differentiation Composition Operators from Mixed-Norm to Zygmund Spaces

“…Liu and Y. Yu We prove that (52) and (56) imply (49). The proof of (50) and (51) is similar, hence it will be omitted.…”

“…Stević in [44] studied the boundedness and compactness of the weighted differentiation composition operator D n ,u from mixed-norm spaces to weighted-type spaces or the little weighted-type space. Zhu in [49] studied the boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces. Yang in [47] studied the boundedness and compactness of the operator C D and DC from Q K (p, q) to and ,0 spaces.…”

“…The products of composition operator and integral-type operators, acting on various spaces of analytic functions, has been recently studied, for example, in [15,16,19,23,42] (see also the related references therein). Motivated by the results [24,32,44,48,49], we consider the boundedness and compactness of the operators D n ,u from H (p, q, ) to the Zygmund space, and the little Zygmund space. For the proof, we need different test functions and some complex calculation skills.…”

Differences of the products of integral type and composition operators fromH∞to the Bloch space

“…Readers interested in composition operators can refer to the books [1] by Shapiro, [2] by Cowen and MacCluer and [3] by Zhu, which are excellent sources for the development of the theory of composition operators and function spaces, and the recent papers for example, [4][5][6][7][8][9][10][11] and other references therein.…”

Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces

“…weighted composition operator by Zhu in [65], and studied in [45,55,[61][62][63][65][66][67][68][69]. The product W ϕ,ψ D n can be regarded as a generalization of W ϕ,ψ D. For some other product-type operators, see, for example, [10,[18][19][20][21][34][35][36][37][38]41,42,44,47,[51][52][53]56,57] and the references therein.…”