与算子相连的面积积分在乘积空间中的有界性

The boundedness of area integrals associated with operators on product domains

本文假设自伴算子L_(1)与L_(2)的热半群满足非对角估计(GGE_(p0)),其中p_(0)∈[1,2).在乘积空间R^(n_(1))×R^(n_(2))中,本文通过自伴算子L_(1)与L_(2)的热半群定义了与算子相连的面积积分S,证明了当p∈(p0,p’0)时,面积积分S在L^(p)(R^(n_(1))×R^(n_(2)))中的有界性.

In this paper,let L_(1) and L_(2) be self-adjoint operators.We assume that e^(-tL_(1))and e^(-tL_(2))satisfy offdiagonal estimates of the type(GGE_(p_(0),m))for some p_(0)∈[1,2)and introduce the area integral S associated with L_(1) and L_(2) on the product space R^(n_(1))×R^(n_(2)).We prove that S is bounded on L^(p) for p∈(p_(0),p'_(0)).