Displaying similar documents to “The quasihyperbolic metric, growth, and John domains.”

On Hardy spaces on worm domains

Alessandro Monguzzi (2016)

Concrete Operators

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In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting...

Hardy and Rellich type inequalities with remainders

Ramil Nasibullin (2022)

Czechoslovak Mathematical Journal

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Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011)...

Bounce trajectories in plane tubular domains

Roberto Peirone (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.

Bounce trajectories in plane tubular domains

Roberto Peirone (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.

Hölder functions in Bergman type spaces

Yingwei Chen, Guangbin Ren (2012)

Studia Mathematica

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It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth...

A note on Costara's paper

Armen Edigarian (2004)

Annales Polonici Mathematici

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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.

Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ

Marco M. Peloso, Hercule Valencourt (2010)

Colloquium Mathematicae

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We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces ℋ p , k ( ) , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.

Elasticity of A + XB[X] when A ⊂ B is a minimal extension of integral domains

Ahmed Ayache, Hanen Monceur (2011)

Colloquium Mathematicae

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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.

Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

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Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with...

Power domains

Karol Borsuk (1972)

Colloquium Mathematicae

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