Heisenberg群上散度型抛物算子的Morrey估计

Morrey Estimates for Divergence Parabolic Operators on the Heisenberg Group

设Heisenberg群上散度型抛物方程的系数是实值有界可测函数,满足一致椭圆条件,且关于X1,X2,…,X2n诱导的拟距离是VMO函数.利用Heisenberg群上的奇异积分及其交换子的Morrey有界性和凝固系数法,研究了散度型抛物方程的弱解在广义Morrey空间中的正则性.

Let the coefficients of the divergence parabolic equation on the Heisenberg group be real valued,bounded measurable VMO functions with respect to a quasidistance induced by vector fields X1,X2,…,X2n and satisfy the uniform elliptic condition.By making use of boundedness of singular integral operators and their commutators on Morrey spaces defined on the Heisenberg group and the freezing coefficients argument,the regularity in Morrey spaces of weak solutions of the divergence parabolic equation is established.