Wang, Shiming A class of maximal operators of Bochner-Riesz means of multiple Fourier series in the fractional integral space. (Chinese. English summary) Zbl 0774.42007 J. Zhejiang Univ. 23, No. 6, 904-911 (1989). Let \(S^ \alpha_ R(f,x)\) denote the Bochner-Riesz means of the Fourier series of \(f(x)\). Let \(C^ p_ \lambda\) be the Riesz potential spaces corresponding to Bessel potential spaces in the nonperiodic case. The purpose of this paper is to set up an approximation result: If \(\alpha>((n-1)/2+\lambda)| 2/p-1|\), \(f\in C^ p_ \lambda\), \(1<p<\infty\), and \(0\leq \lambda\leq 2\), then \(\| S^ \alpha_ R f- f\|_ p=O(R^{-\lambda})\). However, the above result is not sharp. In fact, the lower bound of \(\alpha\) can be reduced. MSC: 42B05 Fourier series and coefficients in several variables 42B25 Maximal functions, Littlewood-Paley theory 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 26A33 Fractional derivatives and integrals 47B38 Linear operators on function spaces (general) Keywords:maximal operators; multiple Fourier series; Bochner-Riesz means; Riesz potential spaces; Bessel potential spaces; approximation PDFBibTeX XMLCite \textit{S. Wang}, J. Zhejiang Univ. 23, No. 6, 904--911 (1989; Zbl 0774.42007)