We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.

中文翻译：

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可变指数福克空间

我们引入了可变指数 Fock 空间并研究了它们的一些基本属性，例如评估函数的有界性、多项式的密度、伯格曼型投影的有界性和对偶性。我们还证明了在全局 log-Hölder 条件下，变指数 Fock 空间与经典空间重合。