Some Problems Of Operator Theory On The Fock-Sobolev Space

In this thesis, we mainly study some properties of the Fock-Sobolev space in Cn, and focus on the reproducing kernel and the carleson measure of the Fock-Sobolev space in Cn. We also establish the boundedness of the weighted Fock projection on appropriate Lp spaces, identify the Banach dual of Fap,m, and compute the complex interpolation space between two Fap,m spaces.In chapter1, we discuss some related research background, and give some basic concepts and notations. At last, we show the significance of research work.In chapter2, we characterize the equivalent condition of the Fock-Sobolev space in Cn.In chapter3, we obtain the orthonormal basis and the reproducing kernel of Fa2,m in Cn.In chapter4, we characterize Carleson-type measures for Fock-Sobolev space in Cn and give the equivalent condition for a positive Borel measure on C" to be Carelson and vanishing Carelson.In chapter5, we determine the Banach dual space and the complex interpolation space of the Fock-Sobolev space in Cn.