Artículos de revistas
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Fecha
2017-09Registro en:
1664-235X
10.1007/s13324-017-0195-3
Autor
Kesler, Robert
Mena Arias, Darío Alberto
Institución
Resumen
Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported
functions
$$
H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}.
$$
We prove that, uniformly in $\alpha \in \bT$, there is a sparse bound for the bilinear form $\inn{H^{\alpha} f}{g}$.
The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse H\"older classes.