Circle packing and interpolation in Fock spaces

It was shown by James Tung in 2005 that if a sequence $Z=\{z_n\}$ of points in the complex plane satisfies $$\inf_{n\not=m}|z_n-z_m|>2/\sqrt\alpha,$$ then $Z$ is a sequence of interpolation for the Fock space $F^p_\alpha$. Using results from circle packing, we show that the constant above can be improved to $$\sqrt{2\pi/(\sqrt3\,\alpha)},$$ which is strictly smaller than $2/\sqrt\alpha$. A similar result will also be obtained for sampling sequences.Comment: 7 page

Fock-Sobolev spaces and their Carleson measures

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.Comment: A revised version has been published in Journal of Functional Analysi

Integral operators induced by the Fock kernel

We study the $L^p$ boundedness and find the norm of a class of integral operators induced by the reproducing kernel of Fock spaces over $C^n$.Comment: 21 page