On the weak (1,1) boundedness of a class of oscillatory singular integrals
Volume 106 / 1993
Studia Mathematica 106 (1993), 279-287
DOI: 10.4064/sm-106-3-279-287
Abstract
We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include $ϕ(x) = e^{-1/x^2}$ and $ϕ(x) = xe^{-1/|x|}$. Some related counterexample is also discussed.
