Lévy-type operators with kernels comparable to log(I-Δ) produce strong hypercontractivity and eventual boundedness with differentiability gains, but not supercontractivity, while more singular kernels smooth instantly and less singular ones do not regularize.
W.Spectral theory of the operator ( p2 + m2)1/2 −Ze 2/r.Communications in Mathematical Physics 53, 3 (Feb
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Gradual smoothing: strong hypercontractivity and logarithmic Sobolev inequalities
Lévy-type operators with kernels comparable to log(I-Δ) produce strong hypercontractivity and eventual boundedness with differentiability gains, but not supercontractivity, while more singular kernels smooth instantly and less singular ones do not regularize.