CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
Tempered distributions and Fourier transform on the Heisenberg group
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Solutions to the fractional Schrödinger equation on the Heisenberg group satisfy time-dependent Hardy space bounds via sub-Laplacian Fourier multipliers, and Bessel potential spaces correspond to Sobolev spaces on this group.
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Non-embeddable torus and CR Paneitz operator
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
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Regularity of fractional Schr\"odinger equations and sub-Laplacian multipliers on the Heisenberg group
Solutions to the fractional Schrödinger equation on the Heisenberg group satisfy time-dependent Hardy space bounds via sub-Laplacian Fourier multipliers, and Bessel potential spaces correspond to Sobolev spaces on this group.