<p>For <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$g\in {{\,\textrm{BMOA}\,}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>∈</mo> <mrow> <mspace width="0.166667em" /> <mtext>BMOA</mtext> <mspace width="0.166667em" /> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we introduce the meromorphic optimal domain <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(T_g,H^p)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mi>g</mi> </msub> <mo>,</mo> <msup> <mi>H</mi> <mi>p</mi> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, i.e. the space containing the meromorphic functions that are mapped under the action of the generalized Volterra operator <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$T_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> into the Hardy space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$H^p$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>. We investigate its properties and characterize for which <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$g_1,g_2 \in {{\,\textrm{BMOA}\,}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>∈</mo> <mrow> <mspace width="0.166667em" /> <mtext>BMOA</mtext> <mspace width="0.166667em" /> </mrow> </mrow> </math></EquationSource> </InlineEquation> the corresponding meromorphic optimal domains coincide. This investigation contributes to a more comprehensive understanding of the holomorphic optimal domain of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$T_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$H^p$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>.</p>

Meromorphic optimal domain of integral operators

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2025年6月30日

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Carlo Bellavita,
Anıl Belli,
Georgios Nikolaidis,
Georgios Stylogiannis

摘要

For $g\in {{\,\textrm{BMOA}\,}}$ $g \in BMOA$ , we introduce the meromorphic optimal domain $(T_g,H^p)$ $(T_{g}, H^{p})$ , i.e. the space containing the meromorphic functions that are mapped under the action of the generalized Volterra operator $T_g$ $T_{g}$ into the Hardy space $H^p$ $H^{p}$ . We investigate its properties and characterize for which $g_1,g_2 \in {{\,\textrm{BMOA}\,}}$ $g_{1}, g_{2} \in BMOA$ the corresponding meromorphic optimal domains coincide. This investigation contributes to a more comprehensive understanding of the holomorphic optimal domain of $T_g$ $T_{g}$ in $H^p$ $H^{p}$ .