The derivative at zero of the conformal fractional Laplacian yields a conformal logarithmic Laplacian whose spectral, stereographic, and Yamabe-type properties are characterized, including an explicit classification of nonnegative weak solutions.
Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere sn., Proceedings of the National Academy of Sciences, 89 (1992), pp
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The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces
The derivative at zero of the conformal fractional Laplacian yields a conformal logarithmic Laplacian whose spectral, stereographic, and Yamabe-type properties are characterized, including an explicit classification of nonnegative weak solutions.