Lacunary discrete spherical maximal functions
Fecha
2019
Tipo
artículo preliminar
Autores
Kesler, Robert
Lacey, Michael T.
Mena Arias, Darío Alberto
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Resumen
We prove new l^p(Z^d) bounds for discrete spherical averages in dimensions d greater than or equal to 5. We focus on the case of lacunary radii, first for
general lacunary radii, and then for certain kinds of highly composite
choices of radii. In particular, if Aλf is the spherical average of f over
the discrete sphere of radius λ, we have for any lacunary sets of integers {λ
2
k}. We follow a style of argument
from our prior paper, addressing the full supremum. The relevant maximal operator is decomposed into several parts; each part requires only
one endpoint estimate.
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MATHEMATICS