On respresentation of derivatives of functions in $L_p$

Abstract

A theorem on the expansion of the derivative $f^{(r_1,r_2,\dots,r_n)}$, where $fın L_p$, and the derivatives of singular integralsinto the series of band-limited functions (entire functions of exponential type), which converges in $L_p$ for $1\le p\le q<ınfty$, is proved.The norms of their items are estimated by best approximations by "an angle''.