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

1 Department of Mathematics - Department of Mathematics 2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Abstract : 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 $-A^{\alpha}$.

Keywords : Dirichlet form. Dirichlet form Ultracontractivity property logarithmic Sobolev inequality Semigroup of operators Fractional powers of operators Nash inequality

Author: Alexander Bendikov - Patrick Maheux -

Source: https://hal.archives-ouvertes.fr/