The Complete (L..., L...) Mapping Properties for a Class of Oscillatory Integrals.
and estimates for oscillatory integrals and their extended domains
We prove the boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
Several characterizations for the special atom spaces with applications.
The theory of functions plays an important role in harmonic analysis. Because of this, it turns out that some spaces of analytic functions have been studied extensively, such as H-spaces, Bergman spaces, etc. One of the major insights that has developed in the study of H-spaces is what we call the real atomic characterization of these spaces.
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