THE WEAK TYPE (1,1) BOUNDS FOR THE MAXIMAL FUNCTION ASSOCIATED TO CUBES GROW TO INFINITY WITH THE DIMENSION
By J. M. Aldaz. 2008
53 citations recorded by the source corpus.
Let Md be the centered Hardy-Littlewood maximal function associated to cubes in R d with Lebesgue measure, and let cd denote the lowest constant appearing in the weak type (1,1) inequality satised by Md. We show that cd ! 1 as d ! 1, thus answering, for the case of cubes, a longstanding
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/f697ffa45084bcf4a57ea16606a8b5f2cab7ae8f
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In Applied Mathematics
- Assaf Naor
- Terence Tao
- Sanghyuk Lee
- D. Tataru
- Zihua Guo
- Jean Bourgain
- Carlos E. Kenig
- Jonathan Bennett
Citations in the corpus
- The Structure of Translation-Invariant Spaces on Locally Compact Abelian Groups (2015, unknown): “However, a remarkable recent result of Aldez [1] shows that weak type (1, 1) bounds of the Hardy-Littlewood maximal operator with respect to centered cubes grow to ∞ as dimension increases.”
- Random Martingales and localization of maximal inequalities (2009, background): “A recent breakthrough of Aldaz [1] showed that when Xn = l n ∞, i.”