A strong convergence theorem for H¹(𝕋ⁿ)

Feng Dai. "A strong convergence theorem for H¹(𝕋ⁿ)." Studia Mathematica 173.2 (2006): 167-184. <http://eudml.org/doc/284920>.

@article{FengDai2006,
abstract = {Let ⁿ denote the usual n-torus and let $S̃_\{u\}^\{δ\}(f)$, 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, $lim_\{R→∞\} 1/log R ∫_\{0\}^\{R\} (||S̃^\{α\}_\{u\}(f) - f||_\{H¹(ⁿ)\})/(u + 1) du = 0$.},
author = {Feng Dai},
journal = {Studia Mathematica},
keywords = {strong convergence; Hardy space ; Bochner-Riesz means; critical index},
language = {eng},
number = {2},
pages = {167-184},
title = {A strong convergence theorem for H¹(𝕋ⁿ)},
url = {http://eudml.org/doc/284920},
volume = {173},
year = {2006},
}

TY - JOUR
AU - Feng Dai
TI - A strong convergence theorem for H¹(𝕋ⁿ)
JO - Studia Mathematica
PY - 2006
VL - 173
IS - 2
SP - 167
EP - 184
AB - Let ⁿ denote the usual n-torus and let $S̃_{u}^{δ}(f)$, 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, $lim_{R→∞} 1/log R ∫_{0}^{R} (||S̃^{α}_{u}(f) - f||_{H¹(ⁿ)})/(u + 1) du = 0$.
LA - eng
KW - strong convergence; Hardy space ; Bochner-Riesz means; critical index
UR - http://eudml.org/doc/284920
ER -