3 research outputs found
Transference of fractional Laplacian regularity
In this note we show how to obtain regularity estimates for the fractional
Laplacian on the multidimensional torus from the fractional
Laplacian on . Though at first glance this may seem quite
natural, it must be carefully precised. A reason for that is the simple fact
that functions on the torus can not be identified with functions on
. The transference is achieved through a formula that holds in
the distributional sense. Such an identity allows us to transfer Harnack
inequalities, to relate the extension problems, and to obtain pointwise
formulas and H\"older regularity estimates.Comment: 7 pages. To appear in Special Functions, Partial Differential
Equations and Harmonic Analysis. Proceedings of the conference in honor of
Calixto P. Calder\'on, Roosevelt University at Chicago, November 16-18, 2012.
C. Georgakis, A. Stokolos and W. Urbina (eds