Year: 2024
Type: preprint
Abstract: We consider the oscillatory integrals with parameter-dependent phases. We decompose the integrals into a leading term and a remainder term. Instead of the pointwise estimate, we use some $L^p$-estimate for the remainder term and get various uniform estimates when the phase functions satisfy certain conditions. This enables us to reduce the requirement of the smoothness on the phase functions, and hence improve the results in \cite[Theorem 7.7.5]{Hormander} and also obtain a refined version of the well-known Van der Corput Lemma. Some applications on the uniform expansion of the Bessel functions and dispersive estimates are also given.
Source: arXiv (Cornell University)
Author: Guo, Zihua
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391833681