Dimension dependency of the weak type (1, 1) bounds for maximal functions associated to finite radial measures

DOI10.1112/blms/bdl027zbMath1133.42026arXivmath/0504240OpenAlexW2110418478MaRDI QIDQ5297601

Jésus M. Aldaz

Publication date: 12 July 2007

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504240

zbMATH Keywords

radial measuresweak type (1, 1) inequalitycentered maximal function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Linear operators on function spaces (general) (47B38) Inequalities for sums, series and integrals (26D15)

Related Items (10)

Weak-type lower bounds for high-dimensional Hardy-Littlewood maximal operators on certain measures via averaging operators ⋮ On high dimensional maximal operators ⋮ Localization and dimension free estimates for maximal functions ⋮ The weak type \((1,1)\) bounds for the maximal function associated to cubes grow to infinity with the dimension ⋮ Bounds for maximal functions associated with rotational invariant measures in high dimensions ⋮ Kissing numbers and the centered maximal operator ⋮ The Stein-Strömberg covering theorem in metric spaces ⋮ Optimal bounds on the modulus of continuity of the uncentered Hardy-Littlewood maximal function ⋮ Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures ⋮ Ornstein–Uhlenbeck operators and semigroups

Cites Work

• Behavior of maximal functions in \(R^ n\) for large n
• A geometric bound for maximal functions associated to convex bodies
• Singular measures and convolution operators
• Sphere packings give an explicit bound for the Besicovitch covering theorem
• On the \(L^ p\)-bounds for maximal functions associated to convex bodies in \({\mathbb{R}}^ n\)
• The development of square functions in the work of A. Zygmund
• An almost-orthogonality principle with applications to maximal functions associated to convex bodies
• On High Dimensional Maximal Functions Associated to Convex Bodies
• A remark on the centered n-dimensional Hardy-Littlewood maximal function

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