Carleson Type Measures for Fock-Sobolev Spaces

We describe the Fock-Carleson measures for weighted Fock-Sobolev spaces in terms of the objects -Berezin transforms, averaging functions, and averaging sequences on the complex space . The main results show that while these objects may have growth not faster than polynomials to induce the measures for , they should be of integrable against a weight of polynomial growth for . As an application, we characterize the bounded and compact weighted composition operators on the Fock-Sobolev spaces in terms of certain Berezin type integral transforms on . We also obtained estimation results for the norms and essential norms of the operators in terms of the integral transforms. The results obtained unify and extend a number of other results in the area.