scholarly journals Sobolev inequalities with jointly concave weights on convex cones

2020 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Cristian E. Gutiérrez ◽  
Alexandru Kristály
Keyword(s):  
Convex Cones ◽  
Sobolev Inequalities

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

scholarly journals Sobolev Inequalities for Functions on Graphs

2021 ◽  
Vol 1804 (1) ◽  
pp. 012132
Author(s):  
Eman Samir Bhaya ◽  
Zainab Flaih
Keyword(s):  
Sobolev Inequalities

scholarly journals Fixed points in convex cones

2017 ◽  
Vol 4 (3) ◽  
pp. 68-93
Author(s):  
Nicolas Monod
Keyword(s):  
Fixed Points ◽  
Convex Cones

scholarly journals Two types of discrete Sobolev inequalities on a weighted Toeplitz graph

2016 ◽  
Vol 507 ◽  
pp. 344-355 ◽  
Author(s):  
Kazuo Takemura ◽  
Atsushi Nagai ◽  
Yoshinori Kametaka
Keyword(s):  
Sobolev Inequalities

scholarly journals Sharp Sobolev inequalities for vector valued maps

2006 ◽  
Vol 253 (4) ◽  
pp. 681-708 ◽  
Author(s):  
Emmanuel Hebey
Keyword(s):  
Sobolev Inequalities ◽  
Vector Valued

Normality and Nuclearity of Convex Cones

Positivity ◽  
2007 ◽  
Vol 11 (3) ◽  
pp. 485-495
Author(s):  
Fatimetou mint El Mounir
Keyword(s):  
Convex Cones

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

scholarly journals Lp-Lq estimates off the line of duality

1995 ◽  
Vol 58 (2) ◽  
pp. 154-166 ◽  
Author(s):  
J.-G. Bak ◽  
D. McMichael ◽  
D. Oberlin
Keyword(s):  
Sobolev Inequalities ◽  
Riesz Means ◽  
Negative Order

AbstractTheorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.

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