A CONDITION FOR LOCAL INTEGRABILITY OF NEGATIVE POWERS OF SMOOTH FUNCTIONS IN TWO VARIABLES - Thi Thao Nguyen (Tạp chí Khoa học Đại học Đà Lạt)
Let f(x,y) be a smooth real-valued function defined in a sufficiently small neighborhood U of the origin such that f(0,0) = 0. We study the set of all positive ε for which $$\int_{U}|f(x,y)|^{-ε}dxdy < ∞.$$ We provide a condition for the Newton polygon characterization such that this set can be expressed in natural ways using the Newton polygon of f .