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arXiv · 2010.04110

Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group

Riju Basak·Rahul Garg·Sundaram Thangavelu
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Abstract

Inspired by the work of A. Bonami and S. Poornima that a non-constant function which is homogeneous of degree $0$ cannot be a Fourier multiplier on homogeneous Sobolev spaces, we establish analogous results for Fourier multipliers on the Heisenberg group $ \mathbb{H}^n $ and Weyl multipliers on $ \mathbb{C}^n $ acting on Sobolev Spaces.

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Riju Basak, Rahul Garg, Sundaram Thangavelu. 2020-10-08. Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group. https://doi.org/10.1016/j.jfa.2021.109154

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