Bases in uniformly convex and uniformly flattened Banach spaces

The aim of this article is to obtain two-sided estimates for the norm of an element $x$ in a uniformly convex and uniformly flattened Banach space $E$ in terms of $l_p$-norms of the sequence of coefficients which occur in the expansion of $x$ in a basis $\{e_i\}^\infty_1$ .