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Fejér means for multivariate Fourier series. (English) Zbl 0904.42009
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.

MSC:
42B08 Summability in several variables
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