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ArticleOriginal scientific text

Title

An oscillatory singular integral operator with polynomial phase

Authors 1, 2

Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-0001, U.S.A.
  2. Departamento de Matemática, UFSCar, São Carlos, 13565-905 SP, Brasil

Abstract

We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space HP1 related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.

Bibliography

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Studia Mathematica
1999/133/1
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Pages:
1-18
Main language of publication
English
Received
1997-05-12
Accepted
1998-07-15
Published
1999
Exact and natural sciences