Volume estimates of sublevel sets of real polynomials
Volume 121 / 2018
Annales Polonici Mathematici 121 (2018), 157-174
MSC: Primary 42B10; Secondary 26D10, 05D99.
DOI: 10.4064/ap170913-25-4
Published online: 9 July 2018
Abstract
We give upper bounds for the volume of sublevel sets of real polynomials. Our method is to combine a version of the global Łojasiewicz inequality with some well known estimates on the volume of tubes around real algebraic sets. Some applications to oscillatory integrals and integration indices of real polynomials are also given.
