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Trudinger inequalities without derivatives

Author(s): Paul MacManus; Carlos Pérez
Journal: Trans. Amer. Math. Soc. 354 (2002), 1997-2012.
MSC (2000): Primary 46E35; Secondary 46E30, 42B25
Posted: January 7, 2002
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Abstract: We prove that the Trudinger inequality holds on connected homogeneous spaces for functions satisfying a very weak type of Poincaré inequality. We also illustrate the connection between this result and the John-Nirenberg theorem for BMO.

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Additional Information:

Paul MacManus
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland
Address at time of publication: Phillips Exeter Academy, 20 Main St., Exeter, New Hampshire 03833
Email: pmacmanus@exeter.edu

Carlos Pérez
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain
Email: carlosperez@us.es

DOI: 10.1090/S0002-9947-02-02918-5
PII: S 0002-9947(02)02918-5
Received by editor(s): March 23, 1999
Received by editor(s) in revised form: July 30, 1999
Posted: January 7, 2002
Additional Notes: Supported by grant ERBFMBICT960939 of the TMR programme of the European Union. This research was carried out during a stay at the Universidad Autónoma de Madrid, and the author wishes to extend his thanks to the Department of Mathematics there.
Research partially supported by DGESIC grant PB98-0106, Spain.
Copyright of article: Copyright 2002, American Mathematical Society

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