Compact operators with BMO symbols on multiply-connected domains

In this paper we study the problem of the boundedness and compactness of the Toeplitz operator Tϕ on L 2 a(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 bound...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Raimondo Roberto
Dokumentumtípus: Cikk
Megjelent: 2018
Sorozat:Acta scientiarum mathematicarum 84 No. 3-4
Kulcsszavak:Operátorok, Operátorelmélet
doi:10.14232/actasm-017-283-0

Online Access:http://acta.bibl.u-szeged.hu/56933
Leíró adatok
Tartalmi kivonat:In this paper we study the problem of the boundedness and compactness of the Toeplitz operator Tϕ on L 2 a(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.
Terjedelem/Fizikai jellemzők:643-658
ISSN:0001-6969