Nash type inequalities for fractional powers of non-negative self-adjoint operators

By A. Bendikov, Patrick Maheux. 2004

59 citations recorded by the source corpus.

Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator$A$, we prove a Nash type inequality for the fractional powers $A^{\alpha}$ of $A$. Under someassumptions, we give ultracontractivity bounds for the semigroup $(T_{t,{\alpha}})$ generated by $-A^{\alpha}$.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f80b5e4ad3d142efa6d6ddab0e15c3ec5b65cec1

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Non-monotone stochastic generalized porous media equations☆ (2008, background): “3 in [2] the Nash inequality holds for fractional Dirichlet forms with parameter d > 0.”
Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, background): “holds for some constant C ′ > 0. By this and again [ 6, Theorem 1.3 ] and (3.1), we have”
An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [3,5,7,39] and the references therein).”
Density and tails of unimodal convolution semigroups (2013, background): “We remark that analogues of the on-diagonal term [ψ−(1/t)]d ≈ pt(0) in (2) are often obtained for more general Markov processes via Nash and Sobolev inequalities [3, 8, 2, 29, 21].”
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, background): “For the special case where f (x) = x , 0 < α < 1, we refer to [9] and to the discussion in [5].”