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Weighted composition operators between Fock spaces \(\mathcal{F}^\infty(\mathbb C)\) and \(\mathcal{F}^p(\mathbb C)\). (English) Zbl 07047452

Summary: In this paper, we establish necessary and sufficient conditions for boundedness and compactness of weighted composition operators acting between Fock spaces \(\mathcal{F}^\infty(\mathbb C)\) and \(\mathcal{F}^p(\mathbb C)\). We also give complete descriptions of path connected components for the space of composition operators and the space of nonzero weighted composition operators in this context.

MSC:

47B33 Linear composition operators
30D15 Special classes of entire functions of one complex variable and growth estimates
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