A Multiplier Theorem on Anisotropic Hardy Spaces

Wang, Li-an Daniel

Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 390-404

Résumé

We present a multiplier theorem on anisotropic Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator ${{T}_{m}}:H_{A}^{p}({{\mathbb{R}}^{n}})\,\to \,H_{A}^{p}({{\mathbb{R}}^{n}})$ , for the range of $p$ that depends on the eccentricities of the dilation $A$ and the level of regularity of a multiplier symbol $m$ . This extends the classical multiplier theorem of Taibleson and Weiss.

Détail

DOI : 10.4153/CMB-2017-029-0

Mots-clés : 42B30, (42B25, 42B35), anisotropic Hardy space, multiplier, Fourier transform