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

Aalto, Daniel

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



Title:	Boundedness of maximal operators and oscillation of functions in metric measure spaces
Author(s):	Aalto, Daniel
Date:	2010
Language:	en
Pages:	Verkkokirja (592 KB, 16 s.)
Department:	Matematiikan ja systeemianalyysin laitos Department of Mathematics and Systems Analysis
ISBN:	978-952-60-3062-3 978-952-60-3061-6 (printed)
Series:	Research reports. Helsinki University of Technology, Institute of Mathematics, A, 585
ISSN:	1797-5867
Supervising professor(s):	Kinnunen, Juha, Prof.
Thesis advisor(s):	Kinnunen, Juha, Prof.
Subject:	Mathematics
Keywords:	doubling measure, maximal functions, discrete convolution, BMO, John-Nirenberg inequality, rearrangements
	OEVS yes
Digitized thesis:	ask
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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.
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].
Permanent link to this item: http://urn.fi/URN:ISBN:978-952-60-3062-3 Email this Export to RefWorks QR Code Print BibTex Tweet

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