2014/08/06 by Hughes, Kevin, Krause, Ben, Trojan, Bartosz
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1408.1213
In this note we prove the following good-λ inequality, for r>2, all λ> 0, δ∈ (0, (1)/(2) ) ν\ Vr(f) gt; 3 λ; M(f) ≤ δλ\ ≤ 4 ν\s(f) gt; δλ\ + δ2 (1+(16)/(r-2))2 ⋅ ν\ Vr(f) gt; λ\, where M(f) is the martingale maximal function, s(f) is the conditional martingale square function. This immediately proves that Vr(f) is bounded on Lp, 1 < p