Extended Cesàro Operators from Mixed Norm Spaces to Zygmund Type Spaces

10.6988/TOJMS.201011.0411

Xiang-Ling Zhu

Mixed norm space ； Zygmund type space ； Extended Cesàro operator

Tamsui Oxford Journal of Mathematical Sciences

26卷4期（2010 / 11 / 01）

411 - 422

英文

Let H(B) denote the space of all holomorphic functions on the unit ball B of C(superscript n) and Rh(z)=Σ(superscript n subscript j)=1 (The equation is abbreviated) (z) the radial derivative of h: In this paper we study the boundedness and compactness of the extended Cesàro operator Tg(f)(z)=∫(superscript 1 subscript 0)f(tz)Rg(tz)dt/t, f∈H(B), z ∈ B, from mixed norm spaces to Zygmund type spaces.