Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Oscillatory singular integrals on $L^{p}$ and Hardy spaces

Author(s): Yibiao Pan
Journal: Proc. Amer. Math. Soc. 124 (1996), 2821-2825.
MSC (1991): Primary 42B20
MathSciNet review: 1328369
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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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