Small ball probabilitiesGaussian Markov processesBrownian motionLet {X(t); 0⩽t⩽1} be a real-valued continuous Gaussian Markov process with mean zero and covariance σ( s, t)= EX( s) X( t)≠0 for 0 0, H>0 and G/ H nondecreasing on the interval (0,1). We show that for ...
We obtain the following strengthened Moser-Trudinger inequality with blow-up analysis for 0 ≤α < λ(Ω) and 1 < p ≤ n, and the supremum is infinity for α≥λ(Ω), whereand ωn1is the surface area of the unit ball in n. We also obtain the existence of the extremal functions ...