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On the compactness of the product of Hankel operators on the sphere

Authors:	Jingbo Xia

Institution:	Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260

Abstract:	Consider Hankel operators $H_\varphi$ and $H_\psi$ on the unit sphere in ${\text{\bf C}}^n$ . If , then a necessary condition for $H^\ast _\varphi H_\psi$ to be compact is $\lim _{\vert z\vert\uparrow 1}\Vert H_\varphi k_z\Vert\Vert H_\psi k_z\Vert = 0$ . We show that when $n \geq 2$ , this condition is no longer necessary for $H^\ast _\varphi H_\psi$ to be compact.

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