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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: 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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Additional Information

Yibiao Pan
Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: yibiao@tomato.math.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03415-6
PII: S 0002-9939(96)03415-6
Received by editor(s): November 15, 1994
Received by editor(s) in revised form: March 25, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society