$$ex supp hat usubset sed{2^{j-2}leq |xi|leq 2^j} a cfrac{1}{C}2^{jk}sen{f}_{L^p} leq sen{D^k f}_{L^p}leq C2^{jk} sen{f}_{L^p}; eex$$ $$ex supp hat usubset sed{|xi|leq 2^j} a sen{f}_{L^q}leq C2^{jnsex{frac{1}{p}-frac{1}{q}}} sen{f}_{L^p}quadsex{1leq pleq qleq infty}. eex$$ see [D. Chae, J. Lee, On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256 (2014), 3835--3858].