CONVOLUTION ESTIMATES FOR SOME MEASURES ON FLAT CURVES

被引：8
|
作者：
BAK, JG
MCMICHAEL, JD
OBERLIN, DM
机构：
[1] Department of Mathematics, Florida State University, Tallahassee
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 1991年 / 101卷 / 01期
关键词：
D O I：
10.1016/0022-1236(91)90149-Y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A measure μ is said to be Lp-improving if μ * Lp ⊂ Lq for some q > p. It is known that certain singular measures supported on curves in R2 are Lp-improving. If μ is a smooth measure supported on a flat curve Γ (the curvature of Γ vanishes to infinite order at some point), μ need not be Lp-improving. Under certain hypotheses, it is proved that in this situation, although μ is not LP-improving, it does satisfy an analogous property with respect to Orlicz spaces: μ * LΦ ⊂ L2 for some Orlicz function Φ with limt → ∝ Φ(t) t2 = 0. Estimates on the distribution function of the Fourier transform of μ are obtained. © 1991.
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页码：81 / 96
页数：16
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