L²-estimates for singular oscillatory integral operators

2015/05/20 by Aleksanyan, Hayk, Shahgholian, Henrik, Sjölin, Per
#35J05 #42B20 #42B25 #47G10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.05348

Abstract

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L² ↦ L² 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 ℝ³.

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