Acta mathematica scientia, Series B >
Sp-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE
Received date: 2011-02-21
Online published: 2012-09-20
Supported by
The research was partly supported by NSFC (10971040).
In this paper, we construct a function u in L2,1(Bn, dA), which is unbounded on any neighborhood of each boundary point of Bn, such that Toeplitz operator Tu is com-pact on Dirichlet space D(Bn, dA). Furthermore, Schatten p-class (0 < p < ∞) Toeplitz operators on Dirichlet space D(Bn, dA) with unbounded symbols are also obtained.
Key words： Toeplitz operator; Dirichlet space; Schatten p-class operator
XIA Jin , WANG Xiao-Feng , CAO Guang-Fu . Sp-CLASS (0 <p < ∞) TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1919 -1928 . DOI: 10.1016/S0252-9602(12)60149-0
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