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arXiv · 1410.3379

Some one-sided estimates for oscillatory singular integrals

Zunwei Fu·Shanzhen Lu·Yibiao Pan·Shaoguang Shi
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Abstract

The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces $H^{1}_{+}(w)$ is proved. It is here also show that the $H^{1}_{+}(w)$ theory of oscillatory singular integrals above cannot be extended to the case of $H^{q}_{+}(w)$ when $0<q<1$ and $w\in A_{p}^{+}$, a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted $L^{p}$-boundednesss of the oscillatory singular integral is given.

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Zunwei Fu, Shanzhen Lu, Yibiao Pan, Shaoguang Shi. 2014-09-20. Some one-sided estimates for oscillatory singular integrals. https://arxiv.org/abs/1410.3379

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