关于A_(r)^(λ_(3))(λ_(1),λ_(2);Ω)-权函数的性质及应用

The property and application for A_(r)^(λ_(3))(λ_(1),λ_(2);Ω)-weight

利用广义Holder不等式及积分技巧,首先证明了双权函数集Ar^λ3(λ1,λ2;Ω)在r>1的条件下关于r的单调不减性。作为Ar^λ3(λ1,λ2;Ω)-权函数的应用,进一步证明了满足Dirac-调和方程的微分形式的加Ar^λ3(λ1,λ2;Ω)-权的范数不等式。若赋予特殊的参数,则可以得到经典权函数的相关结果。

The property of monotonic nondecreasing is proved for the set of Ar^λ3(λ1,λ2;Ω)-two weights under the condition r>1 by generalized Holder inequality and some integral skills. As application of Ar^λ3(λ1,λ2;Ω)-weights, some norm inequalities with Ar^λ3(λ1,λ2;Ω)-weights are obtained which applies to differential forms that satisfying Dirac-harmonic equation. Some results with classical weights will be obtained if special parameters are chosen.