Toeplitz Operators On Analytic Besov Spaces Of Several Complex Variables And On Bergman Spaces In Unit Polydiscs

In this paper,we characterize complex measuresμon the unit ball for which the Toeplitz operator Tμis bounded or compact on the analytic Besov spaces Bp with 1≤p<∞;and we construct bounded or compact Toeplitz operators on the Bergman space La2 in unit polydiscs,whose symbols are unbounded functions.These operators can be Hilbert-Schmidt.And we show that Toeplitz operators on the Bergman space La2 with symbol of essentially unbounded function h=χΓH is compact.In introduction, We have briefly retrospected the historical background and de-veloping processes of the theory of Toeplitz operators, and also introduced the purpose of research and the primary contents of this paper.In chapter two, We have introduced in detail Toeplitz operators on the Bergman space,carleson type measure,shilov boundary and so on.In chapter three,we studied the sufficient and necessary conditions of the Toeplitz operator Tμα, which is bounded or compact.In chapter four, We have obtained bounded or compact Toeplitz operators on the Bergman space La2 in unit polydiscs,whose symbols are unbounded func-tions.These operators can be Hilbert-Schmidt.And we show that Toeplitz operators on the Bergman space La2 with symbol of essentially unbounded function h=χΓH is compact.In the last chapter,some to-be-solved problems is throwed out.