Trace inequalities for operators associated to regular Dirichlet forms

2004 ◽  
Vol 16 (3) ◽  
Author(s):  
Ali Ben Amor
Keyword(s):  
Dirichlet Forms ◽  
Trace Inequalities ◽  
Inequalities For Operators

scholarly journals Some trace inequalities for operators

1995 ◽  
Vol 58 (2) ◽  
pp. 281-286 ◽  
Author(s):  
Xinmin Yang
Keyword(s):  
Positive Definite ◽  
Positive Definite Operators ◽  
Open Question ◽  
Trace Inequalities ◽  
Inequalities For Operators

AbstractIn this paper, we obtain some trace inequalities for arbitrary finite positive definite operators. Finally an open question is presented.

scholarly journals Some inequalities associated with the Hermite-Hadamard inequalities for operator h-convex functions

2017 ◽  
Vol 21 (2) ◽  
Author(s):  
V. Darvish ◽  
S. S. Dragomir ◽  
H. M. Nazari ◽  
A. Taghavi
Keyword(s):  
Convex Functions ◽  
Linear Maps ◽  
Positive Linear Maps ◽  
Trace Inequalities ◽  
Inequalities For Operators

We introduce the concept of operator h-convex functions for positive linear maps, and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain several trace inequalities for operators.

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces

2020 ◽  
Vol 23 (5) ◽  
pp. 1452-1471
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Fractional Integrals ◽  
Mixed Norm ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient ◽  
Bounded Sets ◽  
Trace Inequalities

Abstract D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneously necessary and sufficient for appropriate trace inequalities. The derived results are new even for multiple Riesz potential operators defined on the product of Euclidean spaces.

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.

Non-bipartiteness of Graphs and the Upper Bounds of Dirichlet Forms

2006 ◽  
Vol 25 (3) ◽  
pp. 259-268
Author(s):  
Yusuke Higuchi ◽  
Tomoyuki Shirai
Keyword(s):  
Dirichlet Forms ◽  
Upper Bounds
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