Carleson Measure And Toeplitz Operators On Fock-Type Space

In this paper,we study problem which the Toeplitz operators commutants on Fock-Sobolev spaces.Moreover,we also discuss the relationship about the FockCarleson measures ? between Fock-type spaces F_?^p(0<p??)and F_?^p(0<q??),as well as the Berezin transform of the positive measure.In Chapter 1,we introduce the development process of the operator theory involved on the Fock-type spaces,and give the prerequisite knowledge required in this paper.At last,we show the main results of the article.In Chapter 2,we obtain the sufficient and necessary conditions that T_? and T_? commute on the Fock-Sobolev spaces with the polyradial polynomial function? with z,z as variables and polynomial bounded functions ?.And also give several interesting examples.In Chapter 3,we show that the(p,q)-Fock-Carleson measure(0<p?q??)of positive Borel measure ? is bounded if and only if the Berezin transform of ?is bounded if and only if the mean value function of ? is bounded;the(p,q)-FockCarleson measure(0<p?q??)of ? vanishies if and only if when |z|??,the Berezin transform of ? converges to 0 if and only if when |z|?? the mean value function of ? converges to 0.Moreover,the(p,q)-Fock-Carleson measure(0<q<p??)of ? is bounded if and only if it vanishies at infinity if and only if the Berezin transform of ? belongs to L^p/(p-q)(dV)if and only if the mean value function of ? belongs to L^p/(p-q)(dV),where L^p/(p-q)(dV)is L¹(dV)when p=?.