首页/论文/1908.01833

arXiv 1908.018332019-08-05math.CA

The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals

João P. G. Ramos

备注：: 19 pages

英文摘要：

We make progress on an interesting problem on the boundedness of maximal modulations of the Hilbert transform along the parabola. Namely, if we consider the multiplier arising from it and restrict it to lines, we prove uniform $L^p$ bounds for maximal modulations of the associated operators. Our methods consist of identifying where to use effectively the polynomial Carleson theorem, and where we can take advantage of the presence of oscillation to obtain decay through the $TT^*$ method.

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