关于一类非齐次A-调和方程解的局部和全局的双权范数不等式

摘要

The properties of the solutions to a kind of the nonhomogeneous A-harmonic equations are studied.Some local and global weighted integral inequalities for the conjugate A-harmonic tensors satisfying the nonhomogeneous A-harmonic equation A(x,g+du)=h+d*vare established.Aλr(Ω)-weight and Ar(λ,Ω)-weight and their properties are introduced,and thereby,[7,Lemma 2.4]is generalized to the local two-weighted versions by using HOlder inequality.At last,by Whitney-coverLemma.these results are extended to the global case.The parameters in these obtained results make the inequalities more general and more flexible,so they can be used broadly.%研究一类非齐次A-调和方程的解的性质,给出一些满足方程A(x,g+du)=h+d*v的共轭A一调和张量的局部和全局的积分不等式.通过引入两类双权-Arλ(Ω)权和Ar(λ,Ω)权,借助于H(o)lder不等式及双权的性质,将文献[7,引理2.4]推广成局部加双权形式.根据whitney-覆盖引理,将局部结果推广到全局范畴.结论中的参数使不等式更一般化,更加灵活、适用.