Recently, I study a book about the Besov space and nonlinear partial differential equations, http://link.springer.com/book/10.1007%2F978-3-642-16830-7, whose authors are Hajer Bahouri, Jean-Yves Chemin and Raphaël Danchin. I have a question on the last line of page 137 and the first line of page 138 of this book, they say "we can deduce that $(\partial_t f^n - g^n)_{n\in N}$ is bounded in $L^\rho([0,T];B^{-m}_{p,\infty})$ for some sufficiently large $m>0$: It suffices..." While I try to prove this conclusion for several days, but I fail. Could anybody give me some advice about it?
I am very very thankful for you!