Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points
نویسندگان
چکیده
We generalize the classical Lebesgue's theorem to multi-dimensional functions. prove that Cesàro means of Fourier series function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge $f$ at each strong Lebesgue point.
منابع مشابه
l1-summability of higher-dimensional Fourier series
It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...
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ژورنال
عنوان ژورنال: Constructive mathematical analysis
سال: 2021
ISSN: ['2651-2939']
DOI: https://doi.org/10.33205/cma.859583