$L^2$-estimates for singular oscillatory integral operators

Abstract

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of $L^2\mapsto L^2$ type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in ${\mathbb{R}}^3$.

References in corpus (1)

• Uniform Lipschitz Estimates in Bumpy Half-Spaces