Singular oscillatory integrals on {\mathbb{R}^n} |
| |
Authors: | M Papadimitrakis I R Parissis |
| |
Institution: | 1. Department of Mathematics, University of Crete, Knossos Avenue, 71409, Heraklion, Crete, Greece 2. Institutionen f?r Matematik, Kungliga Tekniska H?gskolan, 100 44, Stockholm, Sweden
|
| |
Abstract: | Let ${\mathcal{P}_{d,n}}Let Pd,n{\mathcal{P}_{d,n}} denote the space of all real polynomials of degree at most d on
\mathbbRn{\mathbb{R}^n} . We prove a new estimate for the logarithmic measure of the sublevel set of a polynomial P ? Pd,1{P\in \mathcal{P}_{d,1}} . Using this estimate, we prove that
supP ? Pd,n| p.v.ò\mathbbRneiP(x)\fracW(x/|x|)|x|ndx| £ c log d (||W||L logL(Sn-1)+1),\mathop{\rm sup}\limits_ {P \in \mathcal{P}_{d,n}}\left| p.v.\int_{\mathbb{R}^{n}}{e^{iP(x)}}{\frac{\Omega(x/|x|)}{|x|^n}dx}\right | \leq c\,{\rm log}\,d\,(||\Omega||_L \log L(S^{n-1})+1), |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|
|