FRACTIONAL FOCK-SOBOLEV SPACES

Let s 2 R and 0 < p 61. The fractional Fock{Sobolev spaces F s;p R are introduced through the fractional radial derivatives R s=2. We describe explicitly the reproducing kernels for the fractional Fock{Sobolev spaces F s;2 R and then get the pointwise size estimate of the reproducing kernels. By using the estimate, we prove that the fractional Fock{Sobolev spaces F s;p R are identified with the weighted Fock spaces F p s that do not involve derivatives. So, the study on the Fock{Sobolev spaces is reduced to that on the weighted Fock spaces.