Fundamental functions of almost greedy bases of $L_p$ for $1<p<\infty$

Abstract

We prove that the fundamental function of any almost greedy basis of $L_p$, $1<p<\infty$, grows as either $(m^{1/p}{)}_{m=1}^{\infty }$ or $(m^{1/2}{)}_{m=1}^{\infty }$.