Lipschitz type characterization of Fock type spaces
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초록
For setting a general weight function on $n$ dimensional complex space $\Cn$, we expand the classical Fock space. We define Fock type space $F^{p,q}_{\phi, t}(\Cn)$ of entire functions with a mixed norm, where $0<p,q<\infty$ and $t\in\R$ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{\phi, t}(\Cn)$. As a result of this application, the space $F^{p,p}_{\phi, t}(\Cn)$ is especially characterized by a Lipschitz type condition.
Abstract
For setting a general weight function on $n$ dimensional complex space $\Cn$, we expand the classical Fock space. We define Fock type space $F^{p,q}_{\phi, t}(\Cn)$ of entire functions with a mixed norm, where $0<p,q<\infty$ and $t\in\R$ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{\phi, t}(\Cn)$. As a result of this application, the space $F^{p,p}_{\phi, t}(\Cn)$ is especially characterized by a Lipschitz type condition.
참고문헌 (10)
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