On an integral operator on the unit ball in

Abstract

Let H(B) denote the space of all holomorphic functions on the unit ball B ⊂ C n . In this paper, we investigate the integral operatorwhere g ∈ H(B) and g(z) = n j=1 z j (∂g/∂z j )(z) is the radial derivative of g. The operator can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of the operator on a-Bloch spaces is considered.

Weighted composition operators from Bergman-type spaces into Bloch spaces

“…This space is called a little Bloch space. For more information on Bloch spaces see, for example [1,8,11,14,15] and the references therein. In [5], Ohno has characterized the boundedness and compactness of weighted composition operators between H ∞ , the Bloch space B and the little Bloch space B 0 .…”

Products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces

“…It makes B w into a Banach space. When w(z) = (1 − |z| 2 ) α , α > 0, then B w = B α is the well-known α-Bloch space (e.g., see [1][2][3][4][5]). …”

“…The operators J g and I g , as well as their n-dimensional generalizations acting on various spaces of analytic functions have been recently studied, for example, in [3,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] (also see the related references therein).…”

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…”