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(英文)

Local and global two-weight norm inequalities for solutions to the nonhomogeneous A-harmonic equation

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-调和张量的局部和全局的积分不等式。通过引入两类双权——Aλr(Ω)权和Ar(λ,Ω)权,借助于H 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。

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^ ＊ v are established. Ar^λ （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 -cover Lemma, 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.