RIEMANN-STIELTJES OPERATORS FROM F(p,q,s) SPACES TO α-BLOCH SPACES ON THE UNIT BALL
نویسنده
چکیده
Let H(B) denote the space of all holomorphic functions on the unit ball B Cn. We investigate the following integral operators: Tg( f )(z)= ∫ 1 0 f (tz) g(tz)(dt/t), Lg( f )(z)= ∫ 1 0 f (tz)g(tz)(dt/t), f H(B), z B, where g H(B), and h(z)= ∑n j=1 zj(∂h/∂zj)(z) is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of two classes of Riemann-Stieltjes operators from general function space F(p,q,s), which includes Hardy space, Bergman space, Qp space, BMOA space, and Bloch space, to α-Bloch space α in the unit ball is discussed in this paper.
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