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Orlicz-Poincare inequalities, maximal functions and A(phi)-conditions
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
2010 (English)In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, ISSN 0308-2105, Vol. 140, 31-48 p.Article in journal (Refereed) Published
Abstract [en]

For a measure mu on R-n (or on a doubling metric measure space) and a Young function phi, we define two versions of Orlicz-Poincare inequalities as generalizations of the usual p-Poincare inequality. It is shown that, on R, one of them is equivalent to the boundedness of the Hardy-Littlewood maximal operator from L-phi(R, mu to L-phi R, mu.), while the other is equivalent to a. generalization of the Muckerthoupt A(p)-condition. While one direction in these equivalences is valid only on R, the other holds in the general setting of doubling metric measure spaces. We also characterize both Orlicz-Poincare inequalities oil metric measure spaces by means of pointwise inequalities involving maximal functions of the gradient.

Place, publisher, year, edition, pages
2010. Vol. 140, 31-48 p.
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-54699DOI: 10.1017/S0308210508000772ISI: 000275801000002OAI: oai:DiVA.org:liu-54699DiVA: diva2:308430
Available from: 2010-04-06 Created: 2010-04-06 Last updated: 2016-05-04

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Björn, Jana

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