Before revision:  For adversarially robust streams, we obtain a (1+\epsilon)-approximation to F_p using \frac{\log n{\epsilon^2}} bits of space for p\in[0,2] and using \frac{1{\epsilon^2}n^{1-2/p}} bits of space for integers p>2. We also obtain an adversarially robust algorithm for the L_2-heavy hitters problem using \frac{\log n{\epsilon^2}} bits of space.
After revision:  For adversarially robust streams, we obtain a (1+\epsilon)-approximation to F_p using \frac{\log n{\epsilon^2}} bits of space for p\in[0,2] and using \frac{1{\epsilon^2}n^{1-2/p}}  \frac{\log n{\epsilon^2}} bits of space.