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Acta Mathematica Vietnamica

On compactness of the ¯-Neumann operator on r-convex domains

icon-email Le Mau Hai , Nguyen Xuan Hong

Abstract

In this paper, we show that on a bounded r-convex domain Ω in Cn such that for every zΩ there exists a complex affine subspace Lz of dimension q1 through z such that LzΩ is a q-peak set with rqn the ¯-Neumann operator Nq,Ω is compact.