<p>We characterize boundedness and compactness of the differences of products of Volterra integral operators <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> (Volterra companion operators <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$J_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation>) and composition operators <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{\varphi }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>φ</mi> </msub> </math></EquationSource> </InlineEquation> between different Fock spaces <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {F}^p(\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="script">F</mi> </mrow> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {F}^q(\mathbb {C})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="script">F</mi> </mrow> <mi>q</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for every <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40306_2025_563_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="91" /> </InlineMediaObject> <EquationSource Format="TEX">$p, q \in (0, \infty ]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

Differences of Products of Volterra Type Operators and Composition Operators Between Fock Spaces

期刊论文
发表日期：

2025年3月7日

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Pham The Hao,
Pham Trong Tien

摘要

We characterize boundedness and compactness of the differences of products of Volterra integral operators $V_g$ $V_{g}$ (Volterra companion operators $J_g$ $J_{g}$ ) and composition operators $C_{\varphi }$ $C_{φ}$ between different Fock spaces $\mathcal {F}^p(\mathbb {C})$ $F^{p} (C)$ and $\mathcal {F}^q(\mathbb {C})$ $F^{q} (C)$ for every $p, q \in (0, \infty ]$ $p, q \in (0, \infty]$ .