Berens, Hubert; Xu, Yuan Fejér means for multivariate Fourier series. (English) Zbl 0904.42009 Math. Z. 221, No. 3, 449-465 (1996). The authors prove an analogue to Fejér’s classical theorem in multivariate \(l-1\) summability. Their attractive result reads as follows: In \(l-1\) summability the Cesàro \((C,2d- 1)\) means of the Fourier series of a function \(f\) in \(C(\mathbb{T}^d)\) converge uniformly to \(f\). In particular, the means define a positive linear polynomial approximate identity on \(C(\mathbb{T}^d)\); the order of summability is best possible in the sense that the \((C,\delta)\) means are not positive for \(0<\delta< 2d-1\).They also discuss the Abel means. Reviewer: L.Leindler (Szeged) Cited in 15 Documents MSC: 42B08 Summability in several variables Keywords:multivariate \(l-1\) summability; Fourier series; Abel means PDFBibTeX XMLCite \textit{H. Berens} and \textit{Y. Xu}, Math. Z. 221, No. 3, 449--465 (1996; Zbl 0904.42009) Full Text: DOI EuDML