Let □ b be the Kohn Laplacian acting on (0, j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, a spectral multiplier theorem of Mihlin–Hörmander type for □ b is proved in the case 0 < j< n- 1. Here we prove an analogous theorem in the exceptional cases j= 0 and j= n- 1 , including a weak type (1, 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstract multivariate multiplier theorem for systems of commuting operators.
Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres / Martini, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 286:3-4(2017), pp. 1539-1574. [10.1007/s00209-016-1813-8]
Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres
Martini A.
2017
Abstract
Let □ b be the Kohn Laplacian acting on (0, j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, a spectral multiplier theorem of Mihlin–Hörmander type for □ b is proved in the case 0 < j< n- 1. Here we prove an analogous theorem in the exceptional cases j= 0 and j= n- 1 , including a weak type (1, 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstract multivariate multiplier theorem for systems of commuting operators.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2949521