On necessary and sufficient conditions for the variable exponent Hardy type inequality

2012/12/10 by Farman Mamedov, Mamedov, Farman
Mathematics · #42A05 #42B35 #43A15 #47B38 #54C35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:42A05 #msc:42B35 #msc:43A15 #msc:47B38 #msc:54C35

paper · pdf · doi:10.48550/arxiv.1212.2076

15 pages

arxiv created 2012/12/10 · arxiv updated 2012/12/11

Abstract

We derive a number of equivalent criterions for the variable exponent Hardy type inequality |(1)/(x)∫₀^xf(t)dt|_L^p(.)(0,1)≤ C|f|_L^p(.)(0,1); f≥ 0. to hold, whenever the exponent p:(0,1)→ (1,∞) is increasing or decreasing near small neighborhood of the origin.

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