Self-improving properties of generalized Poincaré type inequalities through rearrangements - Lerner, Andrei K.; Pérez, Carlos (MATHEMATICA SCANDINAVICA, 2005)
We prove, within the context of spaces of homogeneous type, L^p and exponential type self-improving properties for measurable functions satisfying the following Poincaré type inequality: 26733 _α((f-α)χ_B)_μ^*(λμ(B)) c_λa(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.