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Oscillatory singular integrals on and Hardy spaces

Authors:	Yibiao Pan

Institution:	Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Abstract:	We consider boundedness properties of oscillatory singular integrals on $L^{p}$ and Hardy spaces. By constructing a phase function, we prove that $H^{1}$ boundedness may fail while $L^{p}$ boundedness holds for all $p \in (1, \infty )$ . This shows that the $L^{p}$ theory and $H^{1}$ theory for such operators are fundamentally different.

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