An oscillatory singular integral operator with polynomial phase

Volume 133 / 1999

Josfina Alvarez, Jorge Hounie Studia Mathematica 133 (1999), 1-18 DOI: 10.4064/sm-133-1-1-18


We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space $H_P^1$ 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.


  • Josfina Alvarez
  • Jorge Hounie

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