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

Alexander Bendikov; Patrick Maheux

doi:10.1090/s0002-9947-07-04020-2

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

Alexander Bendikov·Patrick Maheux

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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 some assumptions, we give ultracontractivity bounds for the semigroup $(T_{t,{\alpha}})$ generated by $-A^{\alpha}$.

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BibTeX RIS

Alexander Bendikov, Patrick Maheux. 2004-03-10. Nash type inequalities for fractional powers of non-negative self-adjoint operators. https://doi.org/10.1090/s0002-9947-07-04020-2

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