Multipliers of integrals of Cauchy - Stieltjes type

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dc.creatorStoilov, Peyo
dc.date2009-01-13
dc.date.accessioned2026-07-07T12:29:00Z
dc.date.available2026-07-07T12:29:00Z
dc.descriptionLet ${\rm {\mathbb G}}$ be a domain with closed rectifiable Jordan curve $\ell $ . Let $K({\rm {\mathbb G}})$ be the space of all analytic functions in ${\rm {\mathbb G}} $ representable by a Cauchy - Stieltjes integral. Let ${\rm {\mathfrak M}}(K)$ be the class of all multipliers of the space $K({\rm {\mathbb G}}).$ In this paper we prove that if $f$ is bounded analytic function on ${\rm {\mathbb G}}$ and $${\kern 1pt} {\kern 1pt} {\kern 1pt} \mathop{ess\sup}\limits_{η\in \ell } \int_{\ell} \frac{|f(ζ)-f(η)|}{|ζ-η|} |dζ|{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} <\infty {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ,$$ then $f\in {\rm {\mathfrak M}}(K)$ . If ${\rm {\mathbb G}}={\rm {\mathbb D}}$ is the unit disc, this theorem was proved for the first time by V. P. Havin. In particular for a smooth curve $\ell $ we prove that if $f'\in E^{p} ({\rm {\mathbb G}}),{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} p>1,$ then $f\in {\rm {\mathfrak M}}(K),$ where $E^{p} ({\rm {\mathbb G}})$ are the spaces of Smirnov.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0901.1810
dc.identifierhttp://arxiv.org/abs/0901.1810
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215729
dc.subjectComplex Variables
dc.subjectFunctional Analysis
dc.subject30E20, 30D50
dc.titleMultipliers of integrals of Cauchy - Stieltjes type
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