退化薛定谔算子的黎斯位势的端点估计

摘要

Letしf(x) =-1/w(x)Σdi,j=1(6)i(aij(·)(6)jf)(x)+ V(x)f(x),where w(x) is a Muckenhoupt weight function,V(x) is a nonnegative potential satisfying the reverse H(o)lder class with respect to the measure w(x)dx,and aij(·) is a real symmetric matrix satisfying λw(x)｜ξ｜2 ≤∑di.j=aij(x)ξiξj ≤ Aw(x)｜ξ｜2.Let (L)-β/2(f) be the Riesz potential associated to (L),we obtain the boundedness from Ld/β(w) into BMOβ/d(L)(w) or BLOβ/d(L)(w).%考虑退化薛定谔算子(ι)的黎斯位势(ι)-β/2(f),得到了(ι)-β/2(f)是ι/β(w)到BMOβ/d(ι)(w)或者BLOβ/d(ι)(w)有界的,其中(ι)f(x)=-1/w(x)∑di,j=1(6)(aij(·)(6)jf)(x)+V(x),(x),W(x)∈A2是经典的Muckenhoupt权函数,V(x)是非负位势函数,关于测度w(x)dx满足反H(o)lder不等式,aij(·)是实对称矩阵,满足λw｜ξ｜2≤∑i,j=1 aij(x)ξiξj≤ ∧w(x)｜ξ｜2.