The frequency function and its connections to the Lebesgue points and the Hardy–Littlewood maximal function

DOI10.3906/mat-1901-41zbMath1420.42016arXiv1901.01011OpenAlexW2908517138WikidataQ127769300 ScholiaQ127769300MaRDI QIDQ5229877

Faruk Temur

Publication date: 19 August 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01011

zbMATH Keywords

Hardy-Littlewood maximal functionLebesgue pointsfrequency function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items

Endpoint regularity of discrete multilinear fractional nontangential maximal functions, Level set estimates for the discrete frequency function, Regularity of general maximal and minimal functions, Sharp total variation results for maximal functions, Regularity of one-sided multilinear fractional maximal functions, Sharp inequalities for maximal operators on finite graphs, Endpoint regularity of discrete multisublinear fractional maximal operators associated with \(\ell^1\)-balls, Endpoint regularity of the discrete multisublinear fractional maximal operators

Cites Work

• Exceptional points for Lebesgue's density theorem on the real line
• The bilinear maximal functions map into \(L^p\) for \(2/3 < p \leq 1\)
• Level set estimates for the discrete frequency function
• Optimal quality of exceptional points for the Lebesgue density theorem
• A rigidity phenomenon for the Hardy–Littlewood maximal function
• On the variation of the Hardy-Littlewood maximal function
• Continuity of the maximal operator in Sobolev spaces
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