Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Amar, Eric"'
Autor:
Amar, Eric
We study the heat equation $\frac{\partial u}{\partial t}-\Delta u=0,\ u(x,0)=\omega (x),$ where $\Delta :=dd^{*}+d^{*}d$ is the Hodge laplacian and $u(\cdot ,t)$ and $\omega $ are $p$-differential forms in the complete Riemannian manifold $(M,g).$ U
Externí odkaz:
http://arxiv.org/abs/2003.03985
Autor:
Amar, Eric
Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^{n}.$ Denote $H^{p}$($\Omega $) the Hardy space of $\Omega .$ Suppose that $S$ is $H^{p}$ interpolating with $p\geq 2.$ Then $S$ has t
Externí odkaz:
http://arxiv.org/abs/1912.01989
Autor:
Amar, Eric
Let $S$ be a sequence of points in ${\mathbb{D}}^{n}.$ Suppose that $S$ is $H^{p}$ interpolating. Then we prove that the sequence $S$ is Carleson, provided that $p>2.$ We also give a sufficient condition, in terms of dual boundedness and Carleson mea
Externí odkaz:
http://arxiv.org/abs/1911.07038
Autor:
Amar, Eric
We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights. As a consequence, under a "weak bounded geometry" hypothesis, we improve classical Sobolev e
Externí odkaz:
http://arxiv.org/abs/1902.08613
Autor:
Amar, Eric
We study the $\bar \partial $-equation first in Stein manifold then in complete K\"ahler manifolds. The aim is to get $L^{r}$ and Sobolev estimates on solutions with compact support. In the Stein case we get that for any $(p,q)$-form $\omega $ in $L^
Externí odkaz:
http://arxiv.org/abs/1902.02724
Autor:
Amar, Eric
Publikováno v:
Rendiconti di Matematica e delle sue applicazioni, Volume 41 (2020), 117 - 154
We study Sobolev estimates for the solutions of parabolic equations acting on a vector bundle, in a complete, compact or non compact, riemannian manifold $M.$ The idea is to introduce geometric weights on $M.$ We get global Sobolev estimates with the
Externí odkaz:
http://arxiv.org/abs/1812.04411
Autor:
Amar, Eric
Publikováno v:
J. Geometric Analysis. 2018
We introduce the Local Increasing Regularity Method (LIRM) which allows us to get from \emph{local} a priori estimates, on solutions $u$ of a linear equation $\displaystyle Du=\omega ,$ \emph{global} ones. As an application we shall prove that if $D$
Externí odkaz:
http://arxiv.org/abs/1803.07811
Autor:
Amar, Eric
We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables methods. This gi
Externí odkaz:
http://arxiv.org/abs/1706.03837
Autor:
Amar, Eric
We introduce Nevanlinna classes associated to non radial weights in the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables methods. This gives alternative proofs and improve
Externí odkaz:
http://arxiv.org/abs/1703.00283
Autor:
Amar, Eric, Thomas, Pascal J.
We use a special version of the Corona Theorem in several variables, valid when all but one of the data functions are smooth, to generalize to the polydisc and to the ball results obtained by El Fallah, Kellay and Seip about cyclicity of non vanishin
Externí odkaz:
http://arxiv.org/abs/1702.00729