Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
نویسندگان
چکیده
It is proved that the maximal operator σ # of the triangular-Fejér-means of a two-dimensional Walsh–Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 < p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σ 2n of a function f ∈ L1 converge a.e. to f . The maximal operator σ # is bounded from the Hardy space H1/2 to the space weak-L1/2 and is not bounded from the Hardy space H1/2 to the space L1/2.
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