Abstract
It is proved that the maximal operator of the triangular Cesàro means of a two-dimensional Fourier series is bounded from the periodic Hardy space \(H_{p}(\mathbb{T}^{2})\) to \(L_{p}(\mathbb{T}^{2})\) for all 2/(2+α)<p≦∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Cesàro means of a function \(f \in L_{1}(\mathbb{T}^{2})\) converge a.e. to f.
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This research was supported by the Hungarian Scientific Research Funds (OTKA) No. K67642.
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Weisz, F. Triangular Cesàro summability of two dimensional Fourier series. Acta Math Hung 132, 27–41 (2011). https://doi.org/10.1007/s10474-011-0095-1
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DOI: https://doi.org/10.1007/s10474-011-0095-1