Abstract
Let denote the space of all holomorphic functions on the unit ball . We investigate the following integral operators: , , , , where , and is the radial derivative of . The operator can be considered as an extension of the Cesaro operator on the unit disk. The boundedness of two classes of Riemann-Stieltjes operators from general function space , which includes Hardy space, Bergman space, space, BMOA space, and Bloch space, to -Bloch space in the unit ball is discussed in this paper.
Highlights
Let z = (z1, . . . , zn) and w = (w1, . . . , wn) be points in the complex vector space Cn and z,w = z1w1 + ¡¡¡ + znwn. (1.1)Let dv stand for the normalized Lebesgue measure on Cn
The operator Jg acting on various function spaces have been studied recently in [1,2,3, 14, 17, 18]
Suppose that g : B C1 is a holomorphic map of the unit ball, for a holomorphic function f, define
Summary
Let dv stand for the normalized Lebesgue measure on Cn. For a holomorphic function f we denote. Let H(B) denote the class of all holomorphic functions on the unit ball. For a,z 3⁄4 B, a = 0, let φa denote the Mobius transformation of B taking 0 to a defined by φa(z) = a. Let 0 < p, s < 1⁄2, n 1 < q < 1⁄2. We call F(p, q,s) general function space because we can get many function spaces, such as BMOA space, Qp space (see [9]), Bergman space, Hardy space, Bloch space, if we take special parameters of p, q,s in the unit disk setting, see [20]. If q + s 1, F(p, q,s) is the space of constant functions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
