Essential norm of Hankel operators on weighted Bergman spaces of strongly pseudoconvex domains

Abstract

Let \(\rho \) be the defining function of a bounded strongly pseudoconvex domain D with smooth boundary in \({\mathbb {C}}^n\). In this paper, we study the essential norm of Hankel operators \(H^\beta _f\) which are considered as operators from weighted Bergman spaces \(A^p(D,|\rho |^\alpha \,dV)\) to \(L^q(D,|\rho |^\beta \,dV)\) with \(1<p\le q<\infty \) and \(-1<\alpha ,\beta <\infty \). For \(f\in L^1(D,|\rho |^\beta \,dV)\), we obtain some quantities in terms of the symbol function f, which are comparable to the essential norm of the Hankel operator \(H^\beta _f\). Furthermore, it is shown that the essential norm of \(H^\beta _f\) is equivalent to the distance norm from itself to compact Hankel operators.