Integration and localization operators on doubling Fock spaces
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In this paper, given some positive Borel measure $\mu$, we characterize the boundedness and compactness of two types of integration operators $T_{\mu}$ and $J_{\mu}$ from $F_{\phi}^{p}$ to $L_{\phi}^{q}$ for $1<p,q<\infty$. We also study the algebraic properties, and equivalent conditions for compactness of weakly localized operators on $F_{\phi}^{p}$ with $0<p<\infty$.
Abstract
In this paper, given some positive Borel measure $\mu$, we characterize the boundedness and compactness of two types of integration operators $T_{\mu}$ and $J_{\mu}$ from $F_{\phi}^{p}$ to $L_{\phi}^{q}$ for $1<p,q<\infty$. We also study the algebraic properties, and equivalent conditions for compactness of weakly localized operators on $F_{\phi}^{p}$ with $0<p<\infty$.