Besov spaces and \(K\)-functionals in \(L_p,\quad 0<p<1\)
The authors investigate Besov spaces and their connection with trigonometric polynomial approximation in \(L_p[- \pi,\pi]\), algebraic polynomial approximation in \(L_p[-1, 1]\), algebraic polynomial approximation in \(L_p(S)\), and entire function of exponential type approximation in \(L_p(R)\), and characterize \(K\)-functionals for certain pairs of function spaces including\break \((L_p[-\pi,\pi], B^\alpha_s(L_p[-\pi, \pi]))\), \((L_p(R), B^\alpha_s(L_p(R)))\), \((L_p[- 1,1], \overline B^\alpha_s(L_p[-1, 1]))\), and\break \((L_p(S), \overset{=} B^\alpha_s(L_p(S)))\), where \(0< s\leq+\infty\), \(0< p< 1\), \(S\) is a simple polytope and \(0<\alpha< r\).
entire function of exponential type approximation
scientific article; zbMATH DE number 1517047
scientific article