On Weak Type Inequalities for Rare Maximal Functions in ℝⁿ

A. M. Stokolos

doi:10.4064/cm104-2-7

On Weak Type Inequalities for Rare Maximal Functions in ℝⁿ

A. M. Stokolos

Mathematical Sciences

DePaul University

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The study of one-dimensional rare maximal functions was started in [5, 4]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we will call it “dyadic crystallization”) to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.

Original language	American English
Journal	Colloquium Mathematicum
Volume	104
DOIs	https://doi.org/10.4064/cm104-2-7
State	Published - 2006

Keywords

Rare Maximal Functions
Weak Type Inequalities

DC Disciplines

Mathematics

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10.4064/cm104-2-7License: Unspecified

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title = "On Weak Type Inequalities for Rare Maximal Functions in ℝⁿ",

abstract = " The study of one-dimensional rare maximal functions was started in [5, 4]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we will call it “dyadic crystallization”) to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function. ",

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AB - The study of one-dimensional rare maximal functions was started in [5, 4]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we will call it “dyadic crystallization”) to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.

KW - Rare Maximal Functions

KW - Weak Type Inequalities

UR - https://doi.org/10.4064/cm104-2-7

U2 - 10.4064/cm104-2-7

DO - 10.4064/cm104-2-7

M3 - Article

SN - 0010-1354

VL - 104

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

ER -

On Weak Type Inequalities for Rare Maximal Functions in ℝⁿ

Abstract

Keywords

DC Disciplines

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