Besov spaces andK-functionals inL p, 0<p<1*

Abstract

We investigate Besov spaces and their connection with trigonometric polynomial approximation inLp[−π,π], algebraic polynomial approximation inLp[−1,1], algebraic polynomial approximation inLp(S), and entire function of exponential type approximation inLp(R), and characterizeK-functionals for certain pairs of function spaces including (Lp[−π,π],Bsa(Lp[−π,π])), (Lp(R),sa(Lp(R))),\((L_p [ - 1,1]\overline B _B^\alpha (L_p [ - 1,1])),\), and\((L_p (S),\overline{\overline B} _B^\alpha (L_p (S))),\), where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.