Analytic mappings of the unit disk which almost preserve hyperbolic area
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this paper, we study analytic self‐maps of the unit disk which distort hyperbolic areas of large hyperbolic disks by a bounded amount. We give a number of characterizations involving angular derivatives, Lipschitz extensions, Möbius distortion, the distribution of critical points and Aleksandrov–Clark measures.
Oleg Ivrii, Artur Nicolau
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Mixed‐norm estimates via the helicoidal method
Mathematika, Volume 70, Issue 3, July 2024.Abstract We prove multiple vector‐valued and mixed‐norm estimates for multilinear operators in Rd$\mathbb {R}^d$, more precisely for multilinear operators Tk$T_k$ associated to a symbol singular along a k$k$‐dimensional space and for multilinear variants of the Hardy‐Littlewood maximal function.
Cristina Benea, Camil Muscalu
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New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications
Mathematische Nachrichten, Volume 297, Issue 4, Page 1407-1443, April 2024.Abstract Given a bounded Lipschitz domain Ω⊂Rn$\Omega \subset \mathbb {R}^n$, Rychkov showed that there is a linear extension operator E$\mathcal {E}$ for Ω$\Omega$, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator E$\mathcal {E}$ and give some applications.
Ziming Shi, Liding Yao
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Modern harmonic analysis: singular integrals, maximal functions and Littlewood-Paley theory
, 2023 Se estudian las herramientas desarrolladas en la década de 1950 por Calderón y Zygmund, las cuales llevaron al nacimiento del análisis armónico moderno. Algunos de estos conceptos son la función maximal de Hardy-Littlewood junto con sus propiedades de acotación en espacios Lp, teoremas de interpolación y, sobre todo, la descomposición de Calderón y ...
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Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D
Communications on Pure and Applied Mathematics, Volume 77, Issue 2, Page 1353-1404, February 2024.Abstract We study a large family of Riesz‐type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain assumptions.
José A. Carrillo, Ruiwen Shu
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The Littlewood–Paley Theory: A Common Thread of Many Works in Nonlinear Analysis
EMS Newsletter, 2019 In this article we present the Littlewood-Paley theory and illustrate the effectiveness of this microlocal analysis tool in the study of partial differential equations, in a context which is the least technical possible.
H. Bahouri
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The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion. [PDF]
Arch Ration Mech Anal, 2022 Disconzi MM, Ifrim M, Tataru D.
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Maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 van Neerven J, Veraar M.
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Imbedding and multiplier theorems for discrete Littlewood-Paley spaces
, 1996 I. Verbitsky
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Littlewood-Paley Theory for Triangle Buildings. [PDF]
J Geom Anal, 2018 Steger T, Trojan B.
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