Best bilinear approximations of the classes \(S_{p,\theta}^\Omega B\) of periodic functions of many variables
The author obtains exact order-estimates for the best bilinear approximation of certain subsets \(S^{\Omega}_{p,\theta}B\) of periodic functions of several variables in the space \(L_q([-\pi,\pi])^d\), under certain restrictions on the parameters \(p\), \(q\) and \(\theta\). For \(1 \leq p <\infty\), the definition of the spaces \(S^{\Omega}_{p,\theta}B\) used by the author is taken (with a slight modification) from [\textit{Y. Sun} and \textit{H. Wang}, Proc. Steklov Inst. Math. 219, 350--371 (1997) and Tr. Mat. Inst. Steklova 219, 356--377 (1997; Zbl 1032.42015)]. For \(p=\infty\), the definition coincides with that of \(S^{\Omega}_{p} H\) in [\textit{N. N. Pustovojtov}, Anal. Math. 20, No. 1, 35--48 (1994; Zbl 0791.42014)].
almost increasing and almost decreasing functions
scientific article; zbMATH DE number 6110014
scientific article