Geodesic
Distributional fractional powers of the Laplacean. Riesz potentials
Studia Mathematica, Tome 135 (1999) no. 3, pp. 253-271 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For different reasons it is very useful to have at one's disposal a duality formula for the fractional powers of the Laplacean, namely, $((-Δ)^α u,ϕ ) = (u,(-Δ)^α ϕ)$, α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean to obtain some properties of the Riesz potentials in a wide class of spaces which contains the $L^p$-spaces.
DOI : 10.4064/sm-135-3-253-271
Keywords: fractional powers, Laplacean operator, Riesz potentials, singular integrals 
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Celso Martínez;  ;  . Distributional fractional powers of the Laplacean. Riesz potentials. Studia Mathematica, Tome 135 (1999) no. 3, pp. 253-271. doi: 10.4064/sm-135-3-253-271

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