设u∈W1p,loc(Ω)是A-调和函数.如果1<s<p<∞,测度μ(z)定义为dμ=w(z)dx,那么存在常数β>1,使得w∈A1r∩ As/p,sβ/(β-1)≤k<p时,有(1/|B|∫B |φ▽u|swdx)1/s≤c(1/|B|∫B|u▽φ| pwdx)1/p.对所有的球或立方体B Rn和所有的φ∈C∞0(Ω)都成立.这里C是一个不依赖于u和▽u的常数.
[1] GARNETT J B. Bounded analytic functions [M]. New York:Academic Press 1970.
[2] IWANIEC T, SBORDONE C. Weak minima of variational integrals [J]. Journal of fur die Reine und Angewandte Mathematik 1994, 454.
[3] SHUSEN DING. Integrability of conugate A-harmonic tensors in Ls(μ)-averaging domains [J]. Journal of Mathematical Analysis and Applications 1996, 203.