Before revision:  Our techniques also give algorithms for F_p moment estimationwith p>2 on arbitrary order insertion-only and turnstile streams, using \frac{1{\varepsilon^{4/p}}\cdot n^{1-2/p}} bits of space and two passes, which is the first optimal multi-pass F_p estimation algorithm up to \log n factors. Finally, we give an improved lower bound of \Omega \frac{1{\varepsilon^2}\cdot n^{1-2/p}} for one-pass insertion-only streams.
After revision:  Our techniques also give algorithms for F_p moment estimationwith p>2 on arbitrary order insertion-only and turnstile streams, using \frac{1{\varepsilon^{4/p}}\cdot n^{1-2/p}} bits of space and two passes, which is the first optimal  \frac{1{\varepsilon^2}\cdot n^{1-2/p}} for one-pass insertion-only streams.