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<p>Given a weight <i>v</i> on an open set <i>G</i> of a Banach space <i>E</i>, the weighted spaces of analytic functions <i>Hv</i>(<i>G</i>) and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Hv_0(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <msub> <mi>v</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and their interpolating sequences are studied. In particular, it is shown that for a large class of weights on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B_E\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mi>E</mi> </msub> </math></EquationSource> </InlineEquation> we have that <i>Hv</i>(<i>G</i>) is naturally isometrically isomorphic to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(Hv_0(G)^{**}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <msub> <mi>v</mi> <mn>0</mn> </msub> <mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mrow /> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>, and that for those weights the interpolating sequences for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Hv(B_E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mi>v</mi> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mi>E</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are completely classified by their boundary behavior either as the interpolating sequences for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Hv_0(B_E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <msub> <mi>v</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mi>E</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> or for the classical Hardy space <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(H^\infty (B_E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mi>E</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Interpolating sequences for weighted spaces of analytic functions on Banach spaces

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Mario P. Maletzki

摘要

Given a weight v on an open set G of a Banach space E, the weighted spaces of analytic functions Hv(G) and \(Hv_0(G)\) H v 0 ( G ) and their interpolating sequences are studied. In particular, it is shown that for a large class of weights on \(B_E\) B E we have that Hv(G) is naturally isometrically isomorphic to \(Hv_0(G)^{**}\) H v 0 ( G ) ∗ ∗ , and that for those weights the interpolating sequences for \(Hv(B_E)\) H v ( B E ) are completely classified by their boundary behavior either as the interpolating sequences for \(Hv_0(B_E)\) H v 0 ( B E ) or for the classical Hardy space \(H^\infty (B_E)\) H ∞ ( B E ) .