复合算子TｏDｏG的Lipschitz和BMO范数不等式

Lipschitz and BMO norm inequalities for the composite operator TｏDｏG

给出作用在微分形式上的同伦算子、Dirac算子和Green算子的定义及Lipschitz与BMO范数的定义。利用同伦算子、Dirac算子与Green算子的复合算子ToDoG作用在微分形式上的Ls范数不等式,证明复合算子ToDoG作用在微分形式上的Lipschitz与BMO范数不等式。利用严格递增凸函数的性质和逆H9lder不等式,建立复合算子ToDoG关于A-调和方程解的Lipschitz与BMO范数比较不等式。

The definitions of the homotopy operator, the Dirac operator and Green＇ s operator on differen- tial forms and the definitions of the Lipschitz and BMO norms are given. The Lipschitz and BMO norm in- equalities for the composite operator T o D o G are proven through applying the L＇norm inequality for the composition of the homotopy operator, the Dirac operator and Green＇ s operator on differential forms. The comparison inequality acting on the solutions of the A-harmonic equations in terms of the Lipschitz and BMO norms is established by the strictly increasing convex function and the reverse HSlder inequality.