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Uniform Bounds for Oscillatory and Polynomial Carleson Operators

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Abstract

We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson operators near a single scale version of the quadratic Carleson operator.

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Acknowledgements

The author is thankful to Christoph Thiele, Pavel Zorin–Kranich and Shaoming Guo for discussions that led to the final form of this manuscript.

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  1. ETH Zürich, D-Math, Rämistrasse 101, 8092, Zürich, Switzerland

    João P. G. Ramos

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  1. João P. G. Ramos
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Correspondence to João P. G. Ramos.

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Communicated by Fabio Nicola.

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Ramos, J.P.G. Uniform Bounds for Oscillatory and Polynomial Carleson Operators. J Fourier Anal Appl 27, 5 (2021). https://doi.org/10.1007/s00041-020-09806-x

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