Boundary properties of analytic and harmonic functions with values in Banach space

Bukhvalov, A. V.; Danilevich, A. A.

doi:10.1007/bf01158129

Cited by 84 publications

(63 citation statements)

References 3 publications

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“…Then f j \F(eie, s)\h(s) dp(s) ¿¡¿<jf \F(e'e , s)\h(s) ^ dp(s) = Jj\F(e'e)\\Ldhdß)^ W\W ■ Hence /It JÛ JF(reie)\\Ldh4l)-<\\F\\f or 0 < r < 1 so that F £ Hx(Lx(hdp)). Since Lx has the analytic RadonNikodym Property [6], this implies that F(re'e) -> F(e'e) a.e. in Lx(hdp) and, further, that F(reie)= [' P(r,6-t)F(eu)^-J-n 2n as a Bochner integral in Lx(hdp), where P is the Poisson kernel.…”

Section: Admissible Spaces and Derivationsmentioning

confidence: 98%

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Untitled

1992

Trans. Amer. Math. Soc.

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Abstract.We continue the study of centralizers on Köthe function spaces and the commutator estimates they generate (see [29]). Our main result is that if A' is a super-reflexive Köthe function space then for every real centralizer Í2 on X there is a complex interpolation scale of Köthe function spaces through X inducing Í2 as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, all real centralizers can be identified with derivatives of complex interpolation processes. We apply our ideas in an appendix to show, for example, that there is a twisted sum of two Hubert spaces which fails to be a (UMD)-space.

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Section: Admissible Spaces and Derivationsmentioning

confidence: 98%

“…If we let <P* = <S>*X -<í>*x then a precisely similar calculation shows that / RF (9).G'(6)dp -4>*(RF (6).G(8)) < KN(0).…”

Section: "+L _imentioning

confidence: 99%

Untitled

1992

Trans. Amer. Math. Soc.

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“…L'espace X a la propriété de Radon-Nikodym analytique, notée RN a, si on a l'égalité H p (D, X) = H p (T, X) pour un p ∈ [1, +∞] ; l'égalité a alors lieu pour tout p ∈ [1, +∞], voir [8].…”

Section: Notations Et Rappelsunclassified

Interpolation des espaces de Hardy vectoriels

Daher¹

2015

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…[H1,Satz 2.7] or [H2, p. 355]. Moreover, PL 1 a (X) = H 1 (X) if and only if X has the analytic Radon-Nikodým property (ARNP), see [Bu, p. 1055] or [BD,p. 105].…”

Section: Composition Operators On Harmonic Hardy Spacesmentioning

confidence: 99%

Composition operators on vector-valued harmonic functions and Cauchy transforms

Laitila¹,

Tylli²

2006

Indiana Univ. Math. J.

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Abstract. Let ϕ be an analytic self-map of the unit disk. The weak compactness of the composition operators Cϕ : f → f •ϕ is characterized on the vector-valued harmonic Hardy spaces h 1 (X), and on the spaces CT (X) of vector-valued Cauchy transforms, for reflexive Banach spaces X. This provides a vector-valued analogue of results for composition operators which are due to Sarason, Shapiro and Sundberg, as well as Cima and Matheson. We also consider the operators Cϕ on certain spaces wh 1 (X) and wCT (X) of weak type by extending an alternative approach due to Bonet, Domański and Lindström. Concrete examples based on minimal prerequisites highlight the differences between h p (X) (respectively, CT (X)) and the corresponding weak spaces.

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Boundary properties of analytic and harmonic functions with values in Banach space

Cited by 84 publications

References 3 publications

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Untitled

Interpolation des espaces de Hardy vectoriels

Composition operators on vector-valued harmonic functions and Cauchy transforms

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