Homeomorphic extension of quasi-isometries for convex domains in $${\mathbb {C}}^d$$ C d and iteration theory
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Annalen"
DOI: 10.1007/s00208-020-01954-1
Abstract: We study the homeomorphic extension of biholomorphisms between convex domains in $${\mathbb {C}}^d$$ C d without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between the Gromov… read more here.
Keywords: domains mathbb; homeomorphic extension; quasi isometries; convex domains ... See more keywords
The $$L^p$$Lp CR Hartogs separate analyticity theorem for convex domains
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-017-1894-z
Abstract: In this note, a very general theorem of the CR Hartogs type is proved for almost generic strictly convex domains in $$\mathbf{C}^{\mathbf{n}}$$Cn with real analytic boundary. Given such a domain D, and given an $$L^p$$Lp… read more here.
Keywords: separate analyticity; theorem; convex domains; hartogs separate ... See more keywords
Weighted and boundary $$L^{p}$$Lp estimates for solutions of the $$\overline{\partial }$$∂¯-equation on lineally convex domains of finite type and applications
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-017-2015-8
Abstract: We obtain sharp weighted estimates for solutions of the equation $$\overline{\partial }u=f$$∂¯u=f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces $$L^{p}(\Omega ,\delta ^{\gamma })$$Lp(Ω,δγ), $$\delta $$δ being the… read more here.
Keywords: finite type; overline partial; estimates solutions; convex domains ... See more keywords
Radon Inversion Problem for Holomorphic Functions on Circular, Strictly Convex Domains
Sign Up to like & getrecommendations! Published in 2021 at "Complex Analysis and Operator Theory"
DOI: 10.1007/s11785-021-01130-6
Abstract: In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with $${\mathcal {C}}^2$$ boundary. We show that given $$p>0$$ and a strictly positive, continuous function $$\Phi $$ on $$\partial… read more here.
Keywords: circular strictly; inversion problem; radon inversion; convex domains ... See more keywords
Zeros Sets of Hp Functions in Lineally Convex Domains of Finite Type in ℂn$ \mathbb {C}^{n}$
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Vietnamica"
DOI: 10.1007/s40306-018-0284-x
Abstract: In this note, we extend N. Th. Varopoulos result on zero sets of Hp functions of strictly pseudo-convex domains in ℂn$\mathbb {C}^{n}$ to lineally convex domains of finite type. read more here.
Keywords: finite type; convex domains; lineally convex; zeros sets ... See more keywords
Upper estimates of Christoffel function on convex domains
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.06.079
Abstract: Abstract New upper bounds on the pointwise behavior of Christoffel function on convex domains in R d are obtained. These estimates are established by explicitly constructing the corresponding “needle”-like algebraic polynomials having small integral norm… read more here.
Keywords: function convex; upper estimates; christoffel function; convex domains ... See more keywords
Reflected stochastic differential equations driven by G-Brownian motion in non-convex domains
Sign Up to like & getrecommendations! Published in 2019 at "Stochastics and Dynamics"
DOI: 10.1142/s0219493719500254
Abstract: In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with [Formula: see text]-Hölder continuous functions. With the help of these results obtained… read more here.
Keywords: stochastic differential; reflected stochastic; brownian motion; non convex ... See more keywords
Symplectic homology of convex domains and Clarke’s duality
Sign Up to like & getrecommendations! Published in 2022 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2021-0025
Abstract: We prove that the Floer complex that is associated with a convex Hamiltonian function on $\mathbb{R}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated with the Fenchel-dual Hamiltonian. This… read more here.
Keywords: symplectic homology; convex domains; convex; domains clarke ... See more keywords
Multivariable isometries related to certain convex domains
Sign Up to like & getrecommendations! Published in 2018 at "Rocky Mountain Journal of Mathematics"
DOI: 10.1216/rmj-2018-48-1-19
Abstract: There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in Cn. We introduce… read more here.
Keywords: class; multivariable isometries; isometries related; convex domains ... See more keywords