In this paper we prove that every Fourier multiplier on the homogeneous Sobolev space is a continuous function. This theorem is a generalization of the result of A. Bonami and S. Poornima for Fourier multipliers, which are homogeneous functions of degree zero.
Dans cet article, nous prouvons que chaque multiplicateur de Fourier sur l’espace homogène de Sobolev est une fonction continue. Notre théorème est une généralisation du résultat de A. Bonami et S. Poornima sur les multiplicateurs de Fourier, qui sont des fonctions homogènes de degré zéro.
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Accepted:
Published online:
Keywords: Fourier multipliers, Sobolev spaces, Riesz product
Mot clés : multiplicateurs de Fourier, espaces de Sobolev, Produits de Riesz
Kazaniecki, Krystian 1; Wojciechowski, Michał 2
@article{AIF_2016__66_3_1247_0, author = {Kazaniecki, Krystian and Wojciechowski, Micha{\l}}, title = {On the continuity of {Fourier} multipliers on the homogeneous {Sobolev} spaces ${\dot{W}^1_1(R^d)}$}, journal = {Annales de l'Institut Fourier}, pages = {1247--1260}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {66}, number = {3}, year = {2016}, doi = {10.5802/aif.3036}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3036/} }
TY - JOUR AU - Kazaniecki, Krystian AU - Wojciechowski, Michał TI - On the continuity of Fourier multipliers on the homogeneous Sobolev spaces ${\dot{W}^1_1(R^d)}$ JO - Annales de l'Institut Fourier PY - 2016 SP - 1247 EP - 1260 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3036/ DO - 10.5802/aif.3036 LA - en ID - AIF_2016__66_3_1247_0 ER -
%0 Journal Article %A Kazaniecki, Krystian %A Wojciechowski, Michał %T On the continuity of Fourier multipliers on the homogeneous Sobolev spaces ${\dot{W}^1_1(R^d)}$ %J Annales de l'Institut Fourier %D 2016 %P 1247-1260 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3036/ %R 10.5802/aif.3036 %G en %F AIF_2016__66_3_1247_0
Kazaniecki, Krystian; Wojciechowski, Michał. On the continuity of Fourier multipliers on the homogeneous Sobolev spaces ${\dot{W}^1_1(R^d)}$. Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1247-1260. doi : 10.5802/aif.3036. https://aif.centre-mersenne.org/articles/10.5802/aif.3036/
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