Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation

Pommerenke, Ch.

doi:10.1007/bf02567392

Cited by 264 publications

(81 citation statements)

References 13 publications

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“…where its symbol g is an analytic function on D. This operator (also called in the literature the Volterra operator or the generalized Cesàro operator) was first considered by Pommerenke [17] and has been widely studied in several recent papers [2,1,24,27]. We will use properties of this operator for a particular choice of the symbol g in order to better describe information for the maximal space of strong continuity in various cases.…”

Section: The Integral Operator T Gmentioning

confidence: 99%

Semigroups of composition operators and integral operators in spaces of analytic functions

Contreras¹,

Díaz-Madrigal²,

Martínez³

et al. 2013

Ann. Acad. Sci. Fenn. Math.

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Abstract. We study the maximal spaces of strong continuity on BM OA and the Bloch space B for semigroups of composition operators. Characterizations are given for the cases when these maximal spaces are V M OA or the little Bloch B 0 . These characterizations are in terms of the weak compactness of the resolvent function or in terms of a specially chosen symbol g of an integral operator T g . For the second characterization we prove and use an independent result, namely that the operators T g are weakly compact on the above mentioned spaces if and only if they are compact.

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Section: The Integral Operator T Gmentioning

confidence: 99%

Semigroups of composition operators and integral operators in spaces of analytic functions

Contreras¹,

Díaz-Madrigal²,

Martínez³

et al. 2013

Ann. Acad. Sci. Fenn. Math.

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show abstract

“…[14] dans le cas du disque unité) que si II^UBMO^P^ <^1 (^ constante universelle), e b est la dérivée d'une représentation conforme de P"*" sur un domaine de C limité par une courbe corde-arc. …”

Section: Position Des Espaces De Hardy Dans L 2 (F)unclassified

Courbes corde-arc et espaces de Hardy généralisés

David¹

1982

Annales De L’institut Fourier

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“…Pommerenke showed that a similar characterization holds for univalent functions in BM OA, see [8] and also [13]:…”

Section: Now a Function In Hmentioning

confidence: 81%

Hardy spaces and twisted sectors for geometric models

Poggi‐Corradini

1996

Trans. Amer. Math. Soc.

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Abstract. We study the one-to-one analytic maps σ that send the unit disc into a region G with the property that λG ⊂ G for some complex number λ, 0 < |λ| < 1. These functions arise in iteration theory, giving a model for the self-maps of the unit disk into itself, and in the study of composition operators as their eigenfunctions. We show that for such functions there are geometrical conditions on the image region G that characterize their rate of growth, i.e. we prove that σ ∈ p<∞ H p if and only if G does not contain a twisted sector. Then, we examine the connection with composition operators, and further investigate the no twisted sector condition. Finally, in the Appendix, we give a different proof of a result of J. Shapiro about the essential norm of a composition operator.

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Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation

Cited by 264 publications

References 13 publications

Semigroups of composition operators and integral operators in spaces of analytic functions

Semigroups of composition operators and integral operators in spaces of analytic functions

Courbes corde-arc et espaces de Hardy généralisés

Hardy spaces and twisted sectors for geometric models

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