On the regularity of the maximal function of a BV function

DOI10.1016/j.jde.2021.07.037zbMath1472.42031arXiv2007.05752OpenAlexW3191853491MaRDI QIDQ1981722

Panu Lahti

Publication date: 6 September 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.05752

zbMATH Keywords

function of bounded variationabsolute continuitySobolev functionquasicontinuitynon-centered maximal function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (1)

The maximal function of the devil's staircase is absolutely continuous

Cites Work

• Unnamed Item
• Fine properties and a notion of quasicontinuity for BV functions on metric spaces
• The BV-capacity in metric spaces
• The Hardy-Littlewood maximal function of a Sobolev function
• Strong approximation of sets of finite perimeter in metric spaces
• The variation of the maximal function of a radial function
• Relaxation of the non-parametric Plateau problem with an obstacle
• Regularity of the Hardy–Littlewood maximal operator on block decreasing functions
• Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
• A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function
• Lebesgue points and capacities via boxing inequality in metric spaces

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