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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 asweighted inequalities in an intersection of Muckenhoupt and reverse H\"olderclasses.

Sparse Bounds for Discrete Quadratic Phase Hilbert Transform