Boundedness of maximal operators and oscillation of functions in metric measure spaces

Daniel Aalto

Research output: ThesisDoctoral ThesisCollection of Articles

Abstract

In this dissertation the action of maximal operators and the properties of oscillating functions are studied in the context of doubling measure spaces. The work consists of four articles, in which boundedness of maximal operators is studied in several function spaces and different aspects of the oscillation of functions are considered. In particular, new characterizations for the BMO and the weak L∞ are obtained.
Translated title of the contributionBoundedness of maximal operators and oscillation of functions in metric measure spaces
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
Supervisors/Advisors
  • Kinnunen, Juha, Supervising Professor
  • Kinnunen, Juha, Thesis Advisor
Print ISBNs978-952-60-3061-6
Electronic ISBNs978-952-60-3062-3
Publication statusPublished - 2010
MoE publication typeG5 Doctoral dissertation (article)

Keywords

  • doubling measure
  • maximal functions
  • discrete convolution
  • BMO
  • John-Nirenberg inequality
  • rearrangements

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