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arXiv · 1707.05484

Sparse domination via the helicoidal method

Cristina Benea·Camil Muscalu
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Abstract

Using exclusively the localized estimates upon which the helicoidal method was built, we show how sparse estimates can also be obtained. This approach yields a sparse domination for multiple vector-valued extensions of operators as well. We illustrate these ideas for an $n$-linear Fourier multiplier whose symbol is singular along a $k$-dimensional subspace of $\Gamma=\lbrace \xi_1+\ldots+\xi_{n+1}=0 \rbrace$, where $k<\dfrac{n+1}{2}$, and for the variational Carleson operator.

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Cristina Benea, Camil Muscalu. 2017-07-18. Sparse domination via the helicoidal method. https://arxiv.org/abs/1707.05484

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