LIPSCHITZ TYPE CHARACTERIZATION OF FOCK TYPE SPACES

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.