Self-improving properties of generalized Poincaré type inequalities through rearrangements
DOI:
https://doi.org/10.7146/math.scand.a-14973Abstract
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.Downloads
Published
2005-12-01
How to Cite
Lerner, A. K., & Pérez, C. (2005). Self-improving properties of generalized Poincaré type inequalities through rearrangements. MATHEMATICA SCANDINAVICA, 97(2), 217–234. https://doi.org/10.7146/math.scand.a-14973
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