We consider the Fock-Sobolev space $F^{ p,m}$ consisting of entire functions $f$ such that $f^{ (m)}$, the $m$-th order derivative of $f$, is in the Fock space $F^p$. We show that an entire function $f$ is in $F^{ p,m}$ if and only if the function $z^mf(z)$ is in $F^p$. We also characterize the Carleson measures for the spaces $F^{ p,m}$, establish the boundedness of the weighted Fock projection on appropriate $L^p$ spaces, identify the Banach dual of $F^{ p,m}$, and compute the complex interpolation space between two $F^{ p,m}$ spaces.
Categories: math.CV math.FA