From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere
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DOI: 10.1016/j.aim.2019.05.003
Abstract: Abstract We prove a sharp multiplier theorem of Mihlin–Hormander type for the Grushin operator on the unit sphere in R 3 , and a corresponding boundedness result for the associated Bochner–Riesz means. The proof hinges… read more here.
Keywords: grushin; spherical harmonics; sharp multiplier; harmonics ... See more keywords
A robust approach to sharp multiplier theorems for Grushin operators
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DOI: 10.1090/tran/7844
Abstract: We prove a multiplier theorem of Mihlin-Hormander type for operators of the form $-\Delta_x - V(x) \Delta_y$ on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_y$, where $V(x) = \sum_{j=1}^{d_1} V_j(x_j)$, the $V_j$ are perturbations of the power law $t… read more here.
Keywords: grushin operators; multiplier theorems; theorems grushin; robust approach ... See more keywords