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Dergiler / Constructive Mathematical Analysis / 2026 / Volume: 4 Issue: 2

Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points

Ferenc Weisz(Eötvös L. University)0000-0002-7766-2745
Sayfa
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Yayın Tarihi
2021-06-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We prove that the Cesàro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge to $f$ at each strong Lebesgue point.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We generalize the classical Lebesgue's theorem to multi-dimensional functions.
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Temel Bulgular & Veri:We generalize the classical Lebesgue's theorem to multi-dimensional functions.
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Sonuç & Katkı:We prove that the Cesàro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge to $f$ at each strong Lebesgue point.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Cesàro summability · strong Hardy-Littlewood maximal function · strong Lebesgue points

Abstract

We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Cesàro means of the Fourier series of the multi-dimensional function $f\in L_1(\log L)^{d-1}(\mathbb{T}^d)\supset L_p(\mathbb{T}^d) (1<p<\infty)$ converge to $f$ at each strong Lebesgue point.

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Bu Makaleye Atıf Yap

Weisz, F. (2021). Unrestricted Cesàro summability of $d$-dimensional Fourier series and Lebesgue points. Constructive Mathematical Analysis, Volume: 4 Issue: 2. https://doi.org/10.33205/cma.859583

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Kaynakça (22)

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