ACTA issues

## Hankel operators on harmonic Bergman spaces of the unit ball

Jie Miao

Acta Sci. Math. (Szeged) 69:1-2(2003), 391-408
2903/2009

 Abstract. Let $B$ denote the open unit ball in ${\msbm R}^n$. We study Hankel operators $H_f$ on harmonic Bergman spaces $L^p_h(B)$ for $1< p< \infty$. We obtain a necessary and sufficient condition for $H_f$ to be bounded or compact on both $L^p_h(B)$ and its dual space. In particular, a necessary and sufficient condition for $H_f$ to be bounded or compact on $L^2_h(B)$ is $f\in\mathop{\rm BMO} ^2$ or $f\in\mathop{\rm VMO} ^2$, respectively. The results of this paper extend those in [9] and [11] and are real-variable analogue of those in [4] and [8]. AMS Subject Classification (1991): 47B35; 47B32, 47B47 Received January 16, 2002, and in revised form August 30, 2002. (Registered under 2903/2009.)