H_x^s类拟微分算子的强Gārding不等式

THE STRONG GARDING INEQUALITY FOR H_x￣s PSEUDO-DIFFERENTIAL OPERATORS

在证明椭圆偏微分方程解的存在性和探求解的正则性时，Ｇａｒｄｉｎｇ不等式起着关键作用．对于无穷次可微象征类的拟微分算子，很多数学家曾研究过并得到了相应的Ｇｒｄｉｎｇ不等式，对于有限次可微象征的拟微分算子，赖绍永１９９１年证明了相应的Ｇｒｄｉｎｇ不等式．对于Ｈ_ｘ~ｓ空间里的拟微分算子，是否有相应的Ｇｒｄｉｎｇ不等式？本文就对Ｈ_ｘ~ｓ空间里的拟微分算子，肯定地回答了这个问题，推广了Ｂｅａｌｓ，Ｆｅｆｆｅｒｍａｎ（１９７３），Ｈｒｍａｎｄｅｒ（１９６６，１９７９）及Ｔａｙｌｏｒ（１９８１）的结果．

The Grding Inequality is key to prove the existence and regularity of solutions for elliptic differential equation. Many mathematicians have studied and obtained the Grding inequality for infinte differential pseudodifferential operators. Lai Shaoyong obtains Grding inequality for a kind of finite differential symbols in 1991. In this paper, we study Grding inequality of Psendo-differential operators with Hxs space.