Best polynomial approximation in Besov spaces

In this paper we study the problem of best polynomial approximation in the Besov spaces Bγ,q∞. The density of the polynomials and a Walsh-type theorem is proved. A generalization of strong uniqueness is given, the so-called α-strong uniqueness (α ⩾ 1). This property of best polynomial approximations is proved in Bγ,q∞ with α = 21−1q. In the case q = 1, the classical strong uniqueness is obtained.