• East Asian mathematical journal
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• 제38권5호
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• pp.643-647
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• 2022

Let F² denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F². We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

• 대한수학회보
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• 제48권6호
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.