Dunkl spectral multipliers with values in UMD lattices

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• 作者：Luc Deleaval^a ; ^{luc.deleaval@u-pem.fr} ; Christoph Kriegler^b ; ^{christoph.kriegler@math.univ-bpclermont.fr}
• 关键词：42A45 ; 42B25 ; 47A60
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：272
• 期：5
• 页码：2132-2175
• 全文大小：726 K
• 卷排序：272

文摘

We show a Hörmander spectral multiplier theorem for A=A0⊗IdYA=A0⊗IdY acting on the Bochner space Lp(Rd,hκ2;Y), where A0A0 is the Dunkl Laplacian, hκ2 a weight function invariant under the action of a reflection group and Y   is a UMD Banach lattice. We follow hereby a transference method developed by Bonami–Clerc and Dai–Xu, passing through a Marcinkiewicz multiplier theorem on the sphere. We hereby generalize works for A0=−ΔA0=−Δ acting on Lp(Rd,dx)Lp(Rd,dx) by Girardi–Weis, Hytönen and others before. We apply our main result to maximal regularity for Cauchy problems involving A.