Let B be the real unit ball in R-n and f c l(N) (B). Given a multi-index,m = (m(1),...,m(n)) of nonnegative integers with vertical bar m vertical bar = N, we set the quantity sup(x epsilon B,y epsilon E(x,r),x not equal y) (1-vertical bar x vertical bar(2))(alpha) (1-vertical bar y vertical bar(2))(beta) (vertical bar partial derivative(m) f(x)-partial derivative(m) f(y)vertical bar/vertical bar x-y vertical bar(gamma) [x,y](1-gamma)), x+y) where 0
