Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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, E-ISSN 1945-001X, 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.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-147260DOI: 10.4310/MRL.2013.v20.n5.a7ISI: 000342635000007Scopus ID: 2-s2.0-84899872834OAI: oai:DiVA.org:kth-147260DiVA: diva2:729646
Note

QC 20140626

Available from: 2014-06-26 Created: 2014-06-25 Last updated: 2017-12-05Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Iakovlev, Alexander S.Strömberg, Jan-Olov
By organisation
Mathematics (Div.)
In the same journal
Mathematical Research Letters
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 94 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf