TY - JOUR
T1 - Self-improving properties of generalized poincaré type inequalities through rearrangements
AU - Lerner, Andrei K.
AU - Pérez, Carlos
PY - 2005
Y1 - 2005
N2 - 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: 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], [12] as well as [2], [3] and [14]. Our method avoids completely the "good-λ" inequality technique and any kind of representation formula.
AB - 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: 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], [12] as well as [2], [3] and [14]. Our method avoids completely the "good-λ" inequality technique and any kind of representation formula.
UR - http://www.scopus.com/inward/record.url?scp=31144470412&partnerID=8YFLogxK
U2 - 10.7146/math.scand.a-14973
DO - 10.7146/math.scand.a-14973
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AN - SCOPUS:31144470412
SN - 0025-5521
VL - 97
SP - 217
EP - 234
JO - Mathematica Scandinavica
JF - Mathematica Scandinavica
IS - 2
ER -