Lipschitz type characterization of fock type spaces

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY(2022)

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摘要
For setting a general weight function on n dimensional complex space C-n, we expand the classical Fock space. We define Fock type space F-phi,t(p,q) (C-n) of entire functions with a mixed norm, where 0 < p; q < infinity and t is an element of R and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on F-phi,t(p,q) (C-n). As a result of this application, the space F-phi,t(p,p) (C-n) is especially characterized by a Lipschitz type condition.
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关键词
Fock type space,norm equivalence,Littlewood-Paley formula,Lipschitz type condition
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