Geodesic
Optimal embeddings of generalized Bessel and Riesz potentials
Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 91-111

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a space of potentials on the $n$-dimensional Euclidean space that are constructed on the basis of rearrangement-invariant spaces (RISs) by means of convolutions with kernels of general form. These spaces include the classical spaces of Bessel and Riesz potentials as particular cases. We examine the integral properties of the potentials and find necessary and sufficient conditions for their embedding in an RIS. Optimal RISs for such embeddings are also described. 
@article{TRSPY_2010_269_a7,
     author = {M. L. Goldman},
     title = {Optimal embeddings of generalized {Bessel} and {Riesz} potentials},
     journal = {Informatics and Automation},
     pages = {91--111},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a7/}
}
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M. L. Goldman. Optimal embeddings of generalized Bessel and Riesz potentials. Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 91-111. http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a7/