Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
The Frank–Lieb approach to sharp Sobolev inequalities
View through CrossRef
Frank and Lieb gave a new, rearrangement-free, proof of the sharp Hardy–Littlewood–Sobolev inequalities by exploiting their conformal covariance. Using this they gave new proofs of sharp Sobolev inequalities for the embeddings [Formula: see text]. We show that their argument gives a direct proof of the latter inequalities without passing through Hardy–Littlewood–Sobolev inequalities, and, moreover, a new proof of a sharp fully nonlinear Sobolev inequality involving the [Formula: see text]-curvature. Our argument relies on nice commutator identities deduced using the Fefferman–Graham ambient metric.
Title: The Frank–Lieb approach to sharp Sobolev inequalities
Description:
Frank and Lieb gave a new, rearrangement-free, proof of the sharp Hardy–Littlewood–Sobolev inequalities by exploiting their conformal covariance.
Using this they gave new proofs of sharp Sobolev inequalities for the embeddings [Formula: see text].
We show that their argument gives a direct proof of the latter inequalities without passing through Hardy–Littlewood–Sobolev inequalities, and, moreover, a new proof of a sharp fully nonlinear Sobolev inequality involving the [Formula: see text]-curvature.
Our argument relies on nice commutator identities deduced using the Fefferman–Graham ambient metric.
Related Results
Dynamical approaches to Sharp Sobolev inequalities
Dynamical approaches to Sharp Sobolev inequalities
Inégalités de Sobolev optimales : approches dynamiques
Les inégalités de Sobolev, depuis leur preuve en 1938, ont été l'objet d'une intense recherche, et ont permis...
Elements of decorative prose in the novel by Alexander Sobolev “Griffins guard the lyre”
Elements of decorative prose in the novel by Alexander Sobolev “Griffins guard the lyre”
The topic of the article is relevant because it considers the specific poetics of the modern neo-modernist work. It is worth noting that the novel “Griffins Guard the Lyre” is a pa...
Health inequalities in post-conflict settings: A systematic review
Health inequalities in post-conflict settings: A systematic review
Conflict can be a primary driver of health inequalities, but its impact on the distribution of social determinants of health is not very well documented. Also, there is limited evi...
YURI SOBOLEV’S CULTURAL CIPHER SYSTEM
YURI SOBOLEV’S CULTURAL CIPHER SYSTEM
This article focuses on Y. Sobolev's artistic work in different media: magazine illustration, independent graphics, animation and video-art, in which he practiced playing with imag...
Krein–Sobolev Orthogonal Polynomials II
Krein–Sobolev Orthogonal Polynomials II
In a recent paper, Littlejohn and Quintero studied the orthogonal polynomials {Kn}n=0∞—which they named Krein–Sobolev polynomials—that are orthogonal in the classical Sobolev space...
Explicit representations of the norms of the Laguerre-Sobolev and Jacobi-Sobolev polynomials
Explicit representations of the norms of the Laguerre-Sobolev and Jacobi-Sobolev polynomials
Abstract
This paper deals with discrete Sobolev orthogonal polynomials with respect to inner products built upon the classical Laguerre and Jacobi measures on the interva...
Sobolev spaces of mappings into manifolds
Sobolev spaces of mappings into manifolds
Espaces de Sobolev à valeurs variétés
Cette thèse s'intéresse à certaines propriétés des espaces de Sobolev d'applications entre variétés. Ces espaces ont fait l'ob...
Time-reversal-symmetry broken quantum spin Hall in Lieb lattice
Time-reversal-symmetry broken quantum spin Hall in Lieb lattice
In this paper, the time-reversal (TR) symmetry broken quantum spin Hall (QSH) in Lieb lattice is investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform e...