Newton polygons and local integrability of negative powers of smooth functions in the plane
Newton polygons and local integrability of negative powers of smooth functions in the plane
复制标题
牛顿多边形和平面上光滑函数负幂的局部可积性
DOI：
10.1090/s0002-9947-05-03664-0
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
M. Greenblatt
中科院分区：
文献类型：
--
作者：
M. Greenblatt
设f(x，y)是f(0，0)=0的任意光滑实值函数。对于原点的一个足够小的邻域U，我们研究了数sup{∈：∫u|f(x，f)|-∈<；∞}。我们知道，有时这个数可以用f的牛顿多边形以一种自然的方式表示。我们给出了牛顿多边形刻画成立的充要条件。文中还分析了积分在最高值处的性质。
Let f(x,y) be any smooth real-valued function with f(0,0) = 0. For a sufficiently small neighborhood U of the origin, we study the number sup{∈: ∫ u |f(x,f)| -∈ < ∞}. It is known that sometimes this number can be expressed in a natural way using the Newton polygon of f. We provide necessary and sufficient conditions for this Newton polygon characterization to hold. The behavior of the integral at the supremal e is also analyzed.