On the continuity of Fourier multipliers on the homogeneous Sobolev spaces W ˙ 1 1 (R d )
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1247-1260
In this paper we prove that every Fourier multiplier on the homogeneous Sobolev space W ˙ 1 1 ( d ) 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 W ˙ 1 1 ( d ) 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.
Received : 2015-01-02
Revised : 2015-06-21
Accepted : 2015-09-10
Published online : 2016-12-14
Classification:  42B15,  43A22
Keywords: Fourier multipliers, Sobolev spaces, Riesz product
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     pages = {1247-1260},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/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. https://aif.centre-mersenne.org/item/AIF_2016__66_3_1247_0/

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