Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. John Srdjan Petrovic

Second Advisor

Dr. Yan-chun James Tung

Third Advisor

Dr. Paul Eenigenburg

Fourth Advisor

Dr. Jim Zhu


In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dvs ), where dvs ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The operator Sa,b,c generalizes the classical Bergman projectionoperator [Special characters omitted.] which is bounded on Lp ([Special characters omitted.] , dvt ) if and only if p = 2. We will also determine the norms of Sa,0,c and Ta,0,c on Lp ([Special characters omitted.] , dvt ).

Access Setting

Dissertation-Open Access