2014/11/29 by Mu-Fa Chen, Chen, Mu-Fa
Mathematics · #26D10 #34L15 #60J60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.CA #math.FA #math.PR #msc:26D10 #msc:34L15 #msc:60J60
paper · pdf · doi:10.48550/arxiv.1412.0076
13 pages, 5 figures, Festschrift Masatoshi Fukushima: In Honor of Masatoshi Fukushima's Sanju. World Scientific, 2015
arxiv created 2014/11/29 · arxiv updated 2014/12/02
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in terms of the L2-theory. A crucial application of a result by Fukushima and Uemura (2003) is included. In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably.