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<p>We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell ^p_A\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>ℓ</mi> <mi>A</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation> of holomorphic functions with coefficients in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell ^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>. This can only happen for measures that place no mass on any Beurling–Carleson set.</p>

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On the cyclic behavior of singular inner functions in Besov and sequence spaces

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  • 发表日期：

    2025年10月30日

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  • Alberto Dayan,
  • Daniel Seco

摘要

We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure. Such singular inner functions are cyclic also in the space \(\ell ^p_A\) ℓ A p of holomorphic functions with coefficients in \(\ell ^p\) ℓ p . This can only happen for measures that place no mass on any Beurling–Carleson set.