Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China ; Department of Mathematics, Hubei University, Wuhan 430062, People's Republic of China
Abstract:
We show that if a bounded analytic semigroup on satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on , then generates a -regularized group on where . We obtain the estimate of () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.