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On estimates of constants for maximal functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

In this work we will study Hardy-Littlewood maximal function and maximal operator, basing on both classical and most up to date works. In the first chapter we will give definitions for different types of those objects and consider some of their most important properties. The second chapter is entirely devoted to an overview of the fundamental properties of Hardy-Littlewood maximal function, which are strong (p, p) and weak (1, 1) inequalities. Here we list the most actual results on this inequalities in correspondence to the way the maximal func-tion is defined. The third chapter presents the theorem on asymptotic behavior of the lower bound of the constant in the weak-type (1, 1) inequality for the maximal function associated with cubes of Rd, then the dimension d tends to infinity. In the last chapter a method forcomputing constant c, appearing in the main theorem of chapter 3, is given.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , vii, 72 p.
TRITA-MAT-A, 2014:09
Keyword [en]
maximal function; harmonic analysis
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-145704ISRN: KTH/MAT/A-14/09-SEISBN: 978-91-7595-186-7OAI: diva2:719790
Public defence
2014-06-16, F3, Lidnatedsvägen 26, KTH, Stockholm, 13:00 (English)

QC 20140527

Available from: 2014-05-27 Created: 2014-05-27 Last updated: 2014-06-12Bibliographically approved

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Iakovlev, Alexander
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