On equivalence of super log Sobolev and Nash type inequalities

Marco Biroli, and Patrick Maheux. "On equivalence of super log Sobolev and Nash type inequalities." Colloquium Mathematicae 137.2 (2014): 189-208. <http://eudml.org/doc/284350>.

@article{MarcoBiroli2014,
abstract = {We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.},
author = {Marco Biroli, Patrick Maheux},
journal = {Colloquium Mathematicae},
keywords = {ultracontractivity; super log Sobolev inequality; Nash type inequality; Orlicz-Sobolev inequality; semigroups of operators; Dirichlet form; heat kernel; infinite-dimensional torus},
language = {eng},
number = {2},
pages = {189-208},
title = {On equivalence of super log Sobolev and Nash type inequalities},
url = {http://eudml.org/doc/284350},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Marco Biroli
AU - Patrick Maheux
TI - On equivalence of super log Sobolev and Nash type inequalities
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 2
SP - 189
EP - 208
AB - We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.
LA - eng
KW - ultracontractivity; super log Sobolev inequality; Nash type inequality; Orlicz-Sobolev inequality; semigroups of operators; Dirichlet form; heat kernel; infinite-dimensional torus
UR - http://eudml.org/doc/284350
ER -