On Morrey spaces of measures: Basic properties and potential estimates
The author deals with the space \(\mu_ p\) of Radon measures \(\mu\) on \({\mathbb{R}}^ n\) such that the total variation \(| \mu |\) satisfies \(| \mu | (B(z,r))\leq cr^{n(1-1/p)}\). He uses the interpolation technique to prove that the Riesz potential \((-\Delta)^{-\alpha /2}\) maps \(\mu_ p\), \(1<p<n/\alpha\), into \(M_ q=\mu_ q\cap L^ 1_{loc}\), \(1/q=1/p-\alpha /n\), although the fact itself is known [see \textit{J. Peetre}, J. Funct. Anal. 4, 71-87 (1969; Zbl 0175.426)]. The \(\mu_ p\to \mu_ p\) estimate for the heat operator with a kernel \((4\pi t)^{-n/2}\exp (-| x|^ 2/4t)\) is also proved. The author remarks that this publication originates from his study of viscous vortex flow in three-dimensional space.
scientific article; zbMATH DE number 4202685