<p>In this paper, we study the asymptotic behavior of singular values of compact Toeplitz and Hankel operators on Fock-type spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$F^2_\Psi $</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi mathvariant="normal">Ψ</mi> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb {C}^d$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. For Toeplitz operators <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$T_\mu $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>μ</mi> </msub> </math></EquationSource> </InlineEquation> induced by positive Borel measure <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>, we characterize the asymptotic behavior of the singular values sequence <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\{s_n(T_\mu )\}_{n=1}^{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mo stretchy="false">{</mo> <msub> <mi>s</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mi>μ</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>∞</mi> </msubsup> </math></EquationSource> </InlineEquation> in terms of the non-increasing rearrangement of the local averaging function and the Berezin transform of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>. For Hankel operators <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$H_f$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> with locally integrable symbols, we establish asymptotic estimates for <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\{s_n(H_f)\}_{n=1}^{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mo stretchy="false">{</mo> <msub> <mi>s</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>H</mi> <mi>f</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>∞</mi> </msubsup> </math></EquationSource> </InlineEquation> via the non-increasing rearrangement of a certain Luecking-type function.</p>

Asymptotic behavior of singular values of Toeplitz and Hankel operators on Fock-type spaces

期刊论文
发表日期：

2026年1月16日

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Wenjie Huang,
Xiaofeng Wang,
Zhicheng Zeng

摘要

In this paper, we study the asymptotic behavior of singular values of compact Toeplitz and Hankel operators on Fock-type spaces $F^2_\Psi $ $F_{Ψ}^{2}$ over $\mathbb {C}^d$ $C^{d}$ . For Toeplitz operators $T_\mu $ $T_{μ}$ induced by positive Borel measure $\mu $ $μ$ , we characterize the asymptotic behavior of the singular values sequence $\{s_n(T_\mu )\}_{n=1}^{\infty }$ ${s_{n} (T_{μ})}_{n = 1}^{\infty}$ in terms of the non-increasing rearrangement of the local averaging function and the Berezin transform of $\mu $ $μ$ . For Hankel operators $H_f$ $H_{f}$ with locally integrable symbols, we establish asymptotic estimates for $\{s_n(H_f)\}_{n=1}^{\infty }$ ${s_{n} (H_{f})}_{n = 1}^{\infty}$ via the non-increasing rearrangement of a certain Luecking-type function.