| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
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 |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |