Journal article

Compact operators with BMO symbols on multiply-connected domains

Roberto Raimondo

ACTA SCIENTIARUM MATHEMATICARUM | UNIV SZEGED, BOLYAI INSTITUTE | Published : 2018

Abstract

In this paper we study the problem of the boundedness and compactness of the Toeplitz operator Tϕ on L2a(Ω), where Ω is a multiply-connected domain and ϕ is not bounded. We find a necessary and sufficient condition when the symbol is BMO. For this class we also show that the vanishing at the boundary of the Berezin transform is a necessary and sufficient condition for compactness. The same characterization is shown to hold when we analyze operators which are finite sums of finite products of Toeplitz operators with unbounded symbols.

University of Melbourne Researchers