RIEMANN-STIELTJES OPERATOR FROM MIXED NORM SPACES TO ZYGMUND-TYPE SPACES ON THE UNIT BALL

Abstract

In this paper, the authors characterize the boundedness and compactness of the following Riemann-Stieltjes operator $$ L_g(f)(z) = \int_0^1 {\cal R} f(tz) g(tz) \, \frac{dt}{t}, z \in B,$$ where ${\cal R} f(z)$ is the radial derivative of function $f$ at $z$, from mixed norm spaces $H(p,\, q,\, \phi)$ to Zygmund-type spaces on the unit ball.