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Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals

Carlos E. Kenig; Wolfgang Staubach — 2007

Studia Mathematica

We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their $L^{p}$ boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.

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