<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> be an irreducible bounded symmetric domain in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb {C}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\alpha >-\,1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>></mo> <mo>-</mo> <mspace width="0.166667em" /> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$1<p,q<\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo><</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> with <Equation ID="Equ45"> <EquationSource Format="TEX">$\begin{aligned} \frac{a(r-1)}{2}<\frac{\alpha +1+\frac{a(r-1)}{2}}{q}<\alpha +1. \end{aligned}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mfrac> <mrow> <mi>a</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> <mo><</mo> <mfrac> <mrow> <mi>α</mi> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>a</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mi>q</mi> </mfrac> <mo><</mo> <mi>α</mi> <mo>+</mo> <mn>1</mn> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>We characterize the bounded little Hankel operators acting from the Bergman space <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$A_\alpha ^p(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mi>α</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\overline{A_\alpha ^q(\Omega )}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mrow> <msubsup> <mi>A</mi> <mi>α</mi> <mi>q</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>. As an application, we give a weak factorization of the Bergman space <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$A^p_\alpha (\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mi>α</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for some <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$p>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

Little Hankel operators between Bergman spaces in bounded symmetric domains

期刊论文
发表日期：

2026年1月12日

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Cheng Yuan

摘要

Let $\Omega $ $Ω$ be an irreducible bounded symmetric domain in $\mathbb {C}^n$ $C^{n}$ . Let $\alpha >-\,1$ $α > - 1$ , $1<p,q<\infty $ $1 < p, q < \infty$ with $\begin{aligned} \frac{a(r-1)}{2}<\frac{\alpha +1+\frac{a(r-1)}{2}}{q}<\alpha +1. \end{aligned}$ $\begin{matrix} \frac{a (r - 1)}{2} < \frac{α + 1 + \frac{a (r - 1)}{2}}{q} < α + 1 . \end{matrix}$ We characterize the bounded little Hankel operators acting from the Bergman space $A_\alpha ^p(\Omega )$ $A_{α}^{p} (Ω)$ to $\overline{A_\alpha ^q(\Omega )}$ $\bar{A_{α}^{q} (Ω)}$ . As an application, we give a weak factorization of the Bergman space $A^p_\alpha (\Omega )$ $A_{α}^{p} (Ω)$ for some $p>1$ $p > 1$ .