Uniform sparse bounds for discrete quadratic phase Hilbert transforms
artículo original
Fecha
2017-09Autor
Kesler, Robert
Mena Arias, Darío Alberto
Metadatos
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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.
External link to the item
10.1007/s13324-017-0195-3Colecciones
- Matemática [230]