Boundedness of maximal operators and oscillation of functions in metric measure spaces
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Aalto-yliopiston teknillinen korkeakoulu |
Doctoral thesis (article-based)
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Authors
Date
2010
Major/Subject
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].