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

Pan, Yibiao

doi:10.1090/S0002-9939-96-03415-6

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.

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