<p>We completely characterize the boundedness and compactness of a class of Berezin-type operators acting from weighted Fock spaces <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$F^p_{\alpha ,w}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>w</mi> </mrow> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation> into Lebesgue spaces <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$L^q(wdv)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>q</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>w</mi> <mi>d</mi> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$0<p,q<\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo><</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, where <i>w</i> is a weight on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathbb {C}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> that satisfies an <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$A_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-type condition. This solves an open problem raised by Zhou et al. (Banach J Math Anal 18:20, 2024). As an application, we obtain the description of the boundedness and compactness of Toeplitz-type operators acting between weighted Fock spaces induced by <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$A_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-type weights.</p>

A class of Berezin-type operators on weighted Fock spaces with $A_{\infty }$-type weights

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发表日期：

2026年2月28日

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Jiale Chen

摘要

We completely characterize the boundedness and compactness of a class of Berezin-type operators acting from weighted Fock spaces $F^p_{\alpha ,w}$ $F_{α, w}^{p}$ into Lebesgue spaces $L^q(wdv)$ $L^{q} (w d v)$ for all $0<p,q<\infty $ $0 < p, q < \infty$ , where w is a weight on $\mathbb {C}^n$ $C^{n}$ that satisfies an $A_{\infty }$ $A_{\infty}$ -type condition. This solves an open problem raised by Zhou et al. (Banach J Math Anal 18:20, 2024). As an application, we obtain the description of the boundedness and compactness of Toeplitz-type operators acting between weighted Fock spaces induced by $A_{\infty }$ $A_{\infty}$ -type weights.

A class of Berezin-type operators on weighted Fock spaces with \(A_{\infty }\)-type weights

摘要