Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-6,
author = {Magali Folch-Gabayet and James Wright},
title = {An estimation for a family of oscillatory integrals},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {89-97},
zbl = {1009.42008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-6}
}
Magali Folch-Gabayet; James Wright. An estimation for a family of oscillatory integrals. Studia Mathematica, Tome 157 (2003) pp. 89-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-1-6/