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arXiv · 1703.08775

Sparse Bounds for Discrete Quadratic Phase Hilbert Transform

Robert Kesler·Darío Mena
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Abstract

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{2 \pi i\alpha m^2} f(n - m)}{m}. $$ We prove that, uniformly in $\alpha \in \mathbb{T}$, there is a sparse bound for the bilinear form $\langle H^{\alpha} f , g \rangle$. The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse H\"older classes.

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Robert Kesler, Darío Mena. 2017-03-26. Sparse Bounds for Discrete Quadratic Phase Hilbert Transform. https://arxiv.org/abs/1703.08775

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