A strong convergence theorem for H¹(𝕋ⁿ)

Feng Dai

Feng Dai

Studia Mathematica, Tome 173 (2006), p. 167-184 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ⁿ denote the usual n-torus and let $S ̃_{u}^{δ} (f)$ , u > 0, denote the Bochner-Riesz means of order δ > 0 of the Fourier expansion of f ∈ L¹(ⁿ). The main result of this paper states that for f ∈ H¹(ⁿ) and the critical index α: = (n-1)/2, $l i m_{R \to \infty} 1 / l o g R \int_{0}^{R} (| | S ̃_{u}^{α} (f) - {f | |}_{H ¹ (ⁿ)}) / (u + 1) d u = 0$ .

Publié le : 2006-01-01

Zbl 1099.42007

EUDML-ID : urn:eudml:doc:284920

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-4,
     author = {Feng Dai},
     title = {A strong convergence theorem for H1(Tn)},
     journal = {Studia Mathematica},
     volume = {173},
     year = {2006},
     pages = {167-184},
     zbl = {1099.42007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-4}
}

Feng Dai. A strong convergence theorem for H¹(𝕋ⁿ). Studia Mathematica, Tome 173 (2006) pp. 167-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-4/