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Lower bounds for the weak type (1, 1) estimate for the maximal function associated to cubes in high dimensions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)In: Mathematical Research Letters, ISSN 1073-2780, Vol. 20, no 5, 907-918 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we will provide the quantitative estimation for the dependence of a lower bound of the Hardy-Littlewood maximal function. This work was inspired by the paper [1] of Stein and Strömberg where general properties of the maximal function were studied. In that work, the increase with the dimension d of the constant Ad that appears in the weak type (1, 1) inequality for the maximal function was proved however no estimation were given. In a recent paper [2], J.M. Aldaz showed that the lowest constant Ad tends to infinity as the dimension d → ∞. In this paper, we improve the result of J.M. Aldaz providing quantitative estimation of Ad ≥ Cd1/4, where C is a constant independent of d.

Place, publisher, year, edition, pages
2013. Vol. 20, no 5, 907-918 p.
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URN: urn:nbn:se:kth:diva-147260DOI: 10.4310/MRL.2013.v20.n5.a7ISI: 000342635000007ScopusID: 2-s2.0-84899872834OAI: diva2:729646

QC 20140626

Available from: 2014-06-26 Created: 2014-06-25 Last updated: 2014-10-27Bibliographically approved

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Iakovlev, Alexander S.Strömberg, Jan-Olov
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