Gaussian estimates and regularized groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Gaussian estimates and regularized groups

Authors:	Quan Zheng Jizhou Zhang

Affiliation:	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 ${T(z)}_{ operatorname{Re}z>0}$ on $L^2({boldsymbol{Omega}} )$ $({boldsymbol{Omega}} subsetmathbf{R} ^n)$ satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on $L^p({boldsymbol{Omega}} )$ , then generates a $(1-A_p)^{-alpha}$ -regularized group on $L^p({boldsymbol{Omega}} )$ where $alpha>2n \|frac{1}{2}-frac{1}{p}\|$ . We obtain the estimate of $(lambda-A_p)^{-1}$ () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.

Keywords:	Gaussian estimate regularized group analytic semigroup differential operator

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文