Lebesgue points and Cesàro summability of higher dimensional Fourier series over a cone
We introduce a new concept of Lebesgue points, the so-called ωLebesgue points, where ω > 0. As a generalization of the classical Lebesgue’s theorem, we prove that the Cesàro means σ a nf of the Fourier series of a multidimensional function f ∈ L1(T d ) converge to f at each ω-Lebesgue point (0 &l...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
|
| Sorozat: | Acta scientiarum mathematicarum
87 No. 3-4 |
| Kulcsszavak: | Fourier-sor, Lebesgue integrál, Analízis - matematikai |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-021-614-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/75852 |
| Tartalmi kivonat: | We introduce a new concept of Lebesgue points, the so-called ωLebesgue points, where ω > 0. As a generalization of the classical Lebesgue’s theorem, we prove that the Cesàro means σ a nf of the Fourier series of a multidimensional function f ∈ L1(T d ) converge to f at each ω-Lebesgue point (0 < ω < α) as n → ∞. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 505-515 |
| ISSN: | 2064-8316 |