Function Spaces and Potential Theory by David R. Adams

By David R. Adams

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But limo choose a so that fRn ri dx = 1. 8) If a number p is fixed so that 0 < p < 6, then lim * g(Y) = a,b-0 17 lim fR" RN (x) g(y - x) dx = g(y) uniformly for lyl ? R if R is large enough. 7) of the weight function n. We observe that if Ix - yi lyl, then IxI z and IxI > Ix - yl. 6) gives that r] * g(y) < 2Lg(y), if Iyl <26, and thus f (n*g)fdy<2L 1 yIsp gfdy 0 and R - oo. 2. Lo-Capacities and Nonlinear Potentials 44 Remark.

If we set f i Ix - yl. 6) gives that r] * g(y) < 2Lg(y), if Iyl <26, and thus f (n*g)fdy<2L 1 yIsp gfdy

Fukushima and H. Kaneko [173]. g. E. lectures by Fukushima [172] and in P. Malliavin [287]. Another probabilistic interpretation of (a, p)-capacity is due to E. B. 7 below. 1. There are several books in potential theory, with emphasis on different parts of the theory. A classical treatise is O. D. Kellogg [244], although it appeared a few years before the modem development started. The little book [428] by J. Wermer is a nice introduction. The books by L. L. Helms [222] and N. S. Landkof [266] are more comprehensive.

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