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Self-improving properties of generalized Poincaré type inequalities through rearrangements

Opened Access Self-improving properties of generalized Poincaré type inequalities through rearrangements
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Autor: Lerner, Andrei K.
Pérez Moreno, Carlos
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2005
Publicado en: Mathematica Scandinavica, 97 (2), 217-234.
Tipo de documento: Artículo
Resumen: We prove, within the context of spaces of homogeneous type, Lp and exponential type selfimproving properties for measurable functions satisfying the following Poincaré type inequality: inf α (f − α)χB ∗ µ λµ(B) ≤ cλa(B). Here, f ∗ µ denotes the non-increasing rearrangement of f , and a is a functional acting on balls B, satisfying appropriate geometric conditions. Our main result improves the work in [11] MacManus, P., and Pérez, C., Generalized Poincaré inequalities: Sharp self-improving properties, Internat. Math. Res. Notices 2 (1998), 101–116, [12] MacManus, P., and Pérez, C., Trudinger’s inequality without derivatives, Trans. Amer. Math. Soc. 354 (2002), 1997–2012, as well as [2] Franchi, B., Pérez, C., and Wheeden, R. L., Self-Improving Properties of John-Nirenberg and Poincaré Inequalities on Spaces of Homogeneous Type, J. Funct. Anal. 153 (1998), 108–146, [3] Hajłasz, P., and Koskela, P., Sobolev meets Poincaré, C. R. Acad. Sci. Paris 320 (1995), 1211–1215 and [14] Oro...
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Cita: Lerner, A.K. y Pérez Moreno, C. (2005). Self-improving properties of generalized Poincaré type inequalities through rearrangements. Mathematica Scandinavica, 97 (2), 217-234.
Tamaño: 125.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42339

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