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<p>Under certain assumptions on the symbols, we give a necessary and sufficient condition for the boundedness of a new class of operators, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3286_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <msub> <mi>ψ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>ψ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>ψ</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>φ</mi> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}$</EquationSource> </InlineEquation>, mapping from the Bloch-type space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3286_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>X</mi> </msub> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{B}(\mathbb{B}_{X})$</EquationSource> </InlineEquation> into the space of bounded holomorphic function <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3286_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mi mathvariant="normal">∞</mi> </msup> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>X</mi> </msub> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$H^{\infty}(\mathbb{B}_{X})$</EquationSource> </InlineEquation> of infinite-dimensional bounded symmetric domains. Moreover, we establish a sufficient condition for the boundedness of the operator <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3286_Article_IEq5.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="225" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <msub> <mi>ψ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>ψ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>ψ</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>φ</mi> </mrow> </msub> <mo>:</mo> <msub> <mi mathvariant="script">B</mi> <mn>0</mn> </msub> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>X</mi> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <msubsup> <mi>H</mi> <mrow> <mi>μ</mi> <mo>,</mo> <mn>0</mn> </mrow> <mi mathvariant="normal">∞</mi> </msubsup> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>X</mi> </msub> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}: \mathcal{B}_{0}(\mathbb{B}_{X})\rightarrow H_{\mu , 0}^{\infty}(\mathbb{B}_{X})$</EquationSource> </InlineEquation>.</p>

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On a new class of operators from the Bloch-type space into \(H^{\infty}(\mathbb{B}_{X})\) of infinite dimensional bounded symmetric domains

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  • 发表日期：

    2025年3月19日

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  • Xiaoman Liu,
  • Yongmin Liu

摘要

Under certain assumptions on the symbols, we give a necessary and sufficient condition for the boundedness of a new class of operators, T ψ 1 , ψ 2 , ψ 3 , φ $T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}$ , mapping from the Bloch-type space B ( B X ) $\mathcal{B}(\mathbb{B}_{X})$ into the space of bounded holomorphic function H ∞ ( B X ) $H^{\infty}(\mathbb{B}_{X})$ of infinite-dimensional bounded symmetric domains. Moreover, we establish a sufficient condition for the boundedness of the operator T ψ 1 , ψ 2 , ψ 3 , φ : B 0 ( B X ) → H μ , 0 ∞ ( B X ) $T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}: \mathcal{B}_{0}(\mathbb{B}_{X})\rightarrow H_{\mu , 0}^{\infty}(\mathbb{B}_{X})$ .