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

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Volume Title

Aalto-yliopiston teknillinen korkeakoulu | Doctoral thesis (article-based)
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Date

2010

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Mcode

Degree programme

Language

en

Pages

Verkkokirja (592 KB, 16 s.)

Series

Research reports. Helsinki University of Technology, Institute of Mathematics, A, 585

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.

Description

Supervising professor

Kinnunen, Juha, Prof.

Thesis advisor

Kinnunen, Juha, Prof.

Keywords

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

Other note

Parts

  • [Publication 1]: D. Aalto, J. Kinnunen, Maximal functions in Sobolev spaces, Sobolev Spaces in Mathematics I, International Mathematical Series, Vol. 8 Maz'ya, Vladimir (Ed.), 25-68, Springer, 2008.
  • [Publication 2]: D. Aalto, J. Kinnunen, The discrete maximal operator in metric spaces, to appear in J. Anal. Math.
  • [Publication 3]: D. Aalto, Weak L∞ and BMO in metric spaces, arXiv:0910.1207 [math.MG].
  • [Publication 4]: D. Aalto, L. Berkovits, O. E. Maasalo, H. Yue, John-Nirenberg lemmas for doubling measures, arXiv0910.1228 [math.FA].

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