Bloch functions on bounded symmetric domains

Chu, Cho-Ho; Hamada, Hidetaka; Honda, Tatsuhiro; Kohr, Gabriela

doi:10.1016/j.jfa.2016.11.005

Cited by 31 publications

(21 citation statements)

References 18 publications

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“…For bounded symmetric domains B E , it was proved that any Bloch function f on B E is Lipschitz for the hyperbolic distance (see [5] and [7]), that is, there exists M > 0 such that for any x, y ∈ B E , |f (x) − f (y)| ≤ M β(x, y).…”

Section: 2mentioning

confidence: 99%

“…In particular, this study includes the unit euclidean ball B n and the polydisc D n . The study of Bloch functions on bounded symmetric domains of infinite dimensional Banach spaces was introduced by Blasco, Galindo and Miralles (see [4]) for the Hilbert case and by Chu, Hamada, Honda and Kohr for general bounded symmetric domains by means of the Kobayashi metric (see [7]). If we consider these domains as the unit ball B E of a JB * −triple E, the corresponding Bloch space is the set of holomorphic functions on B E which satisfy that sup x∈B E Q f (z) < ∞.…”

Section: 4mentioning

confidence: 99%

“…Automorphisms on E = (C n , · ∞ ) and E = c 0 . Bloch functions on the finite or infinite polydisc were studied in [17] and [7] respectively. In these works, the authors deal with the natural Bloch seminorm · nat and compare it with the invariant Bloch seminorm · inv in the case of a Hilbert space E. Now we prove that the spaces defined with each of these seminorms are different even if B E is the bidisc D 2 .…”

Section: 21mentioning

confidence: 99%

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Bloch functions on the unit ball of a Banach space

Miralles

2021

Proc. Amer. Math. Soc.

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The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions f on the unit ball BE of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch space considering the boundness of (1− x 2 ) f ′ (x) on BE and by preserving the invariance of the correspondiing seminorm when we compose with automorphisms ϕ of BE. We study the connection between these spaces proving that they are different in general and prove that all bounded analytic functions on BE are Bloch functions in both ways.2010 Mathematics Subject Classification. Primary 30D45, 46E50. Secondary 46G20.

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Section: 2mentioning

confidence: 99%

Section: 4mentioning

confidence: 99%

Section: 21mentioning

confidence: 99%

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Bloch functions on the unit ball of a Banach space

Miralles

2021

Proc. Amer. Math. Soc.

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“…Let

H^{\infty} false(B_{X} false) = {f \in H false(B_{X}, double-struckC false) : {∥ f ∥}_{\infty} < + \infty}

be the space, called the Hardy space, of bounded and holomorphic functions on

B_{X}

. When the target is the unit disc in

double-struckC

, Chu, Hamada, Honda and Kohr obtained the following Schwarz Pick lemma (cf. [, Theorem 4.2], [, Theorem 4.6]).…”

Section: Preliminariesmentioning

confidence: 99%

“…Timoney gave several equivalent definitions for Bloch functions on a finite dimensional bounded homogeneous domain. Chu, Hamada, Honda and Kohr generalized the Bloch space to a bounded symmetric domain realized as the open unit ball of a JB*‐triple X . We remark that all four types of classical Cartan domains are the open unit balls of JB*‐triples, and the same holds for any finite product of these Cartan domains (, see also ).…”

Section: Introductionmentioning

confidence: 99%

Operators from the Hardy space to the α‐Bloch space

Honda

2019

Mathematische Nachrichten

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Let BX be a bounded symmetric domain realized as the open unit ball of a finite dimensional JB*‐triple X. In this paper, we characterize the bounded weighted composition operators from the Hardy space H∞false(BXfalse) into the α‐Bloch space scriptBαfalse(BXfalse) on BX. Also, we show the multiplication operator from H∞false(BXfalse) into scriptBαfalse(BXfalse) is bounded. Finally, we show that there exist no isometric composition operators.

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Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces

Hamada

2023

Mathematische Nachrichten

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Let double-struckBH$\mathbb {B}_H$ be the unit ball of a complex Hilbert space H. First, we give a Bohr's inequality for the holomorphic mappings with lacunary series with values in complex Hilbert balls. Next, we give several results on Bohr's inequality for pluriharmonic mappings with values in ℓ2. Note that the Bohr phenomenons that we have obtained are completely different from those in the case with values in C$\mathbb {C}$ and are sharp in the case with values in ℓ2.

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Bloch functions on bounded symmetric domains

Cited by 31 publications

References 18 publications

Bloch functions on the unit ball of a Banach space

Bloch functions on the unit ball of a Banach space

Operators from the Hardy space to the α‐Bloch space

Bohr's inequality for holomorphic and pluriharmonic mappings with values in complex Hilbert spaces

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