Abstract
We study averages along the integers using the divisor function , defined as
where . We shall show that these averages satisfy a uniform, scale free -improving estimate for , that is
as long as is supported on .
We will also show that the associated maximal function satisfies sparse bounds for , which implies that is bounded on for , for all weights in the Muckenhoupt class.
Citation
Christina Giannitsi. "AVERAGING WITH THE DIVISOR FUNCTION: -IMPROVING AND SPARSE BOUNDS." Rocky Mountain J. Math. 52 (6) 2027 - 2039, December 2022. https://doi.org/10.1216/rmj.2022.52.2027
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