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.
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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.