scholarly journals On Hardy spaces on worm domains

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Alessandro Monguzzi
Keyword(s):  
Sobolev Spaces ◽  
Hardy Spaces ◽  
Pseudoconvex Domain ◽  
Bergman Projection ◽  
Review Article ◽  
High Order ◽  
Worm Domains

AbstractIn 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 of non-smooth worm domains.

Mapping properties of the Bergman projections on elementary Reinhardt domains

2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang
Keyword(s):  
Sobolev Spaces ◽  
Bergman Projection ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Multi Index ◽  
Bergman Projections

Abstract The elementary Reinhardt domain associated to multi-index k = (k 1, …, k n ) ∈ ℤ n is defined by ℋ ( k ) : = { z ∈ D n : z k   is defined and   | z k | < 1 } . $$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

scholarly journals Irregularity of the Bergman projection on worm domains in ℂ n

2012 ◽  
Vol 61 (1) ◽  
pp. 187-198 ◽  
Author(s):  
David Barrett ◽  
Sönmez Şahutoğlu
Keyword(s):  
Bergman Projection ◽  
Worm Domains

scholarly journals Embedding relations and boundedness of the multifunctional operators in tube domains over symmetric cones

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 109-126 ◽  
Author(s):  
Milos Arsenovic ◽  
Romi Shamoyan
Keyword(s):  
Hardy Spaces ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Symmetric Cones ◽  
Mixed Norm ◽  
Sufficient Condition ◽  
General Sufficient Condition ◽  
Tube Domains

We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings. We also obtain some sharp embedding relations between the generalized Hilbert-Hardy spaces and the mixed-norm Bergman spaces in this setting.

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

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Xiaming Chen ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Lipschitz Domain ◽  
Lipschitz Domains ◽  
Regularity Estimates ◽  
Bounded Lipschitz Domain ◽  
Divergence Equation ◽  
Strongly Lipschitz Domain

AbstractLet 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 suitable regularity estimates.

Characterizations of anisotropic high order Sobolev spaces

2019 ◽  
Vol 113 (4) ◽  
pp. 239-260
Author(s):  
Nguyen Lam ◽  
Ali Maalaoui ◽  
Andrea Pinamonti
Keyword(s):  
Sobolev Spaces ◽  
High Order

Back to the Barre, Brian Barry

1978 ◽  
Vol 8 (1) ◽  
pp. 119-127
Author(s):  
Gabriel A. Almond ◽  
Scott C. Flanagan
Keyword(s):  
Review Article ◽  
High Order

Brian Barry has a critical talent of a high order. He often executes elegant ballet steps which take the breath away; but occasionally he trips over his own feet and falls into the orchestra pit, making a dreadful racket. His long review article on Crisis, Choice, and Change which appeared in the January and April (1977) numbers of this Journal is one of these unfortunate accidents.

scholarly journals Sharp singular Adams inequalities in high order Sobolev spaces

2012 ◽  
Vol 19 (3) ◽  
pp. 243-266 ◽  
Author(s):  
Nguyen Lam ◽  
Guozhen Lu
Keyword(s):  
Sobolev Spaces ◽  
High Order
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