Self-improving properties of generalized Poincare type inequalities through rearrangements

• Autores: A. K. Lerner
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 97, Nº 2, 2005, págs. 217-234
• Idioma: inglés
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• Resumen

  • We prove, within the context of spaces of homogeneous type, Lp and exponential type self-improving properties for measurable functions satisfying the following Poincaré type inequality: 26733 \inf_{\alpha}\bigl((f-\alpha)\chi_{B}\bigr)_{\mu}^*\bigl(\lambda\mu(B)\bigr) \le c_{\lambda}a(B). 26733 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], [12] as well as [2], [3] and [4]. Our method avoids completely the "good-λ" inequality technique and any kind of representation formula.