Geodesic
Optimal embeddings of generalized Bessel and Riesz potentials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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{TM_2010_269_a7,
     author = {M. L. Goldman},
     title = {Optimal embeddings of generalized {Bessel} and {Riesz} potentials},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {91--111},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_269_a7/}
}
TY  - JOUR
AU  - M. L. Goldman
TI  - Optimal embeddings of generalized Bessel and Riesz potentials
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2010
SP  - 91
EP  - 111
VL  - 269
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2010_269_a7/
LA  - ru
ID  - TM_2010_269_a7
ER  - 
%0 Journal Article
%A M. L. Goldman
%T Optimal embeddings of generalized Bessel and Riesz potentials
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2010
%P 91-111
%V 269
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2010_269_a7/
%G ru
%F TM_2010_269_a7
M. L. Goldman. Optimal embeddings of generalized Bessel and Riesz potentials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 91-111. http://geodesic.mathdoc.fr/item/TM_2010_269_a7/