复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.

Weighted Homotopy Formulas on a Local q-Convex Wedge in a Complex Manifold

In this paper, we obtain a weighted homotopy formula of the (r, s) differential forms and a weighted continuous solution to the -equation of type (r, s) on a local q-convex wedge in a complex manifold. A new weighted homotopy formula without boundary integral of the (r, s) differential forms and a new weighted continuous solution to the -equation of type (r, s), which are different from the classical ones, are given. The new weighted formulas are especially suitable for the case of a local q-convex wedge with non-smooth boundary, so one can avoid complex estimates of the boundary integrals, and the density of integral may not be defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.