On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball

Abstract

We introduce the following integral-type operator on the space H(B) of all holomorphic functions on the unit ball Bwhere g ∈ H(B), g(0) = 0 and ϕ is a holomorphic self-map of B. The boundedness and compactness of the operator from the Bloch space B or the little Bloch space B 0 to the Bloch-type space B μ or the little Bloch-type space B μ,0 , are characterized. In the main results we calculate the essential norm of the operators P g ϕ : B (or B 0 ) → B μ (or B μ,0 ) in an elegant way.

On an integral-type operator from the Bloch space into the QK(p,q) space

“…Some related results can be found, for example, in [5,7,8,13,16,17,19,30,31]. For related operators in n-dimensional case, see [9,15,18,[20][21][22].…”

Compact differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces

“…It is of interest to provide function theoretic characterizations when u and u induce bounded or compact weighted composition operators. For some other products of linear operators related to composition and integral-type operators, see also [14,16,24,25,[27][28][29][30]32,33,36,37,[39][40][41][42]46,52,55].…”

Products of integral-type and composition operators from generally weighted Bloch space to F(p,q,s) space

“…For some information on the operators I φ and J φ and their n-dimensional extensions, see, for example [6,7,8,9,13,14,16,18,19,20,21,22,24,25,26] as well as the related references therein. Let g ∈ H(D) and ϕ be a holomorphic self-map of D. Products of integral and composition operators on H(D) were introduced by S. Li and S. Stević (see [6], [11], [12], [15], as well as closely related operators in [10] and [23]) as follows…”

“…For the case of the unit ball the operator C ϕ J g has been recently extended by Stević in [25] (see also [24], [26]). …”