Inverse theorem for best polynomial approximation in L_p 0< p< 1

TA direct theorem for best polynomial approximation of a function in L_p,0< p< 1 has recently been established. Here we present a matching inverse theorem. In particular, we obtain as a corollary the equivalence for 0 < α < k between The present result complements the known direct and inverse theorem for best polynomial approximation in Analogous results for approximating periodic functions by trigonometric polynomials in L_p[π, π] 0 < p ≤ ∞ are known.