CLT for Lp moduli of continuity of Gaussian processes

Let G={G(x),x[set membership, variant]R1} be a mean zero Gaussian process with stationary increments and set [sigma]2(x-y)=E(G(x)-G(y))2. Let f be a symmetric function with Ef2([eta])<[infinity], where [eta]=N(0,1). When [sigma]2(s) is concave or when [sigma]2(s)=sr, 1<r<=3/2, where [Phi](h,[sigma](h),f,a,b) is the variance of the numerator. This result continues to hold when [sigma]2(s)=sr, 3/2<r<2, for certain functions f, depending on the nature of the coefficients in their Hermite polynomial expansion. The asymptotic behavior of [Phi](h,[sigma](h),f,a,b) at zero is described in a very large number of cases.