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Article overview
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On the endpoint regularity of discrete maximal operators | Emanuel Carneiro
; Kevin Hughes
; | Date: |
6 Sep 2013 | Abstract: | Given a discrete function $f:^d o R$ we consider the maximal operator
$$Mf(vec{n}) = sup_{rgeq0} frac{1}{N(r)} sum_{vec{m} in ar{Omega}_r}
ig|f(vec{n} + vec{m})ig|,$$ where $ig{ar{Omega}_rig}_{r geq 0}$
are dilations of a convex set $Omega$ (open, bounded and with Lipschitz
boudary) containing the origin and $N(r)$ is the number of lattice points
inside $ar{Omega}_r$. We prove here that the operator $f mapsto
abla M f$
is bounded and continuous from $l^1(^d)$ to $l^1(^d)$. We also prove the
same result for the non-centered version of this discrete maximal operator. | Source: | arXiv, 1309.1535 | Services: | Forum | Review | PDF | Favorites |
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