Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSobolev functions on infinite-dimensional domains
191
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.
rate research
Read More
We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.
In this paper we build up a criteria for fractional Orlicz-Sobolev extension and imbedding domains on Ahlfors $n$-regular domains.
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for Schrodinger equation. Inspired by the operators arising in quantum mechanics, in this paper we investigate the continuity of a class of infinite order differential operators acting on spaces of entire hyperholomorphic functions. The two classes of hyperholomorphic functions, that constitute a natural extension of functions ofone complex variable to functions of paravector variables are illustrated by the Fueter-Sce-Qian mapping theorem. We show that, even though the two notions of hyperholomorphic functions are quite different from each other, entire hyperholomorphic functions with exponential bounds play a crucial role in the continuity of infinite order differential operators acting on these two classes of entire hyperholomorphic functions. We point out the remarkable fact that the exponential function of a paravector variable is not in the kernel of the Dirac operator but entire monogenic functions with exponential bounds play an important role in the theory.
If Poincar{e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkovs argument and super-Poincar{e} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.
We study functions of bounded variation (and sets of finite perimeter) on a convex open set $Omegasubseteq X$, $X$ being an infinite dimensional real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semigroup associated with a perturbation of the Ornstein--Uhlenbeck operator.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
