Toeplitz Operators With Unbounded Symbols In Function Spaces

Bergman space, Toeplitz operators as active branch in operator theory not onlyclosely link to many branches of mathematics, but also closely to the other disci-pline,especially in wavelet analysis. Over the last decade, it has been found thatsome classic problem about function theory and operator theory are closely related toBergman space. For example,invariant problem. Many interesting problem aboutcomplex analysis and differential equations have been arising in the study of Bergmanspace and Toeplitz operator. This makes scholars be more and more interested instudying the Toeplitz operators. In this paper, we mainly study Toeplitz operatorswith unbounded symbols in function spaces.In the second chapter, we firstly extend the case of Toeplitz operators with un-bounded symbols in the unit ball to the case of polydisk, and then we also extend thecase of Toeplitz operators with BMO symbols in the unit disk to the case of the unitball. In the third chapter, we extend the result of Toeplitz operators with unboundedsymbols on Dirichlet spaces to the weighted Dirichlet spaces, and study the case ofthem in general Dirichlet spaces.