Decay estimates for weighted oscillatory integrals in ℝ2

Malabika Pramanik, Chan Woo Yang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we study decay estimates for a two-dimensional scalar oscillatory integral with degenerate real-analytic phase and amplitude. Integrals such as these form a model for certain higher-dimensional degenerate oscillatory integrals, for which it is known that many of the two-dimensional results fail. We define an analogue of the Newton distance in the weighted case, and prove that this gives the optimal rate of decay for the weighted oscillatory integral under certain generic hypotheses. When these hypotheses fail, we provide counterexamples to show that the optimal rate of decay may be faster in general. We have obtained bounds for the rate of decay in some of these exceptional cases.

Original languageEnglish
Pages (from-to)613-645
Number of pages33
JournalIndiana University Mathematics Journal
Volume53
Issue number2
DOIs
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • Oscillation index
  • Oscillatory integrals
  • Resolution of singularities
  • Weighted integrals

ASJC Scopus subject areas

  • Mathematics(all)

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