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

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

2004-03-10

arxiv.org/abs/math/0403174v1

Transaction of the American Mathematical Society. 359, 7 (2007) 3085-3097

Mathematics

Spectral Theory

January,31 (2002). Submitted

Scientific paper

10.1090/S0002-9947-07-04020-2

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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