Oscillatory singular integrals on $L^p$ and Hardy spaces
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- by Yibiao Pan
- Proc. Amer. Math. Soc. 124 (1996), 2821-2825
- DOI: https://doi.org/10.1090/S0002-9939-96-03415-6
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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.References
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Bibliographic Information
- Yibiao Pan
- Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- Email: yibiao@tomato.math.pitt.edu
- Received by editor(s): November 15, 1994
- Received by editor(s) in revised form: March 25, 1995
- Communicated by: J. Marshall Ash
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2821-2825
- MSC (1991): Primary 42B20
- DOI: https://doi.org/10.1090/S0002-9939-96-03415-6
- MathSciNet review: 1328369