Geodesic
Description of the interpolation spaces for a~pair of local Morrey-type spaces and their generalizations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 105-137

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

The real interpolation method is considered and it is proved that for general local Morrey-type spaces, in the case in which they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. This result is a particular case of the interpolation theorem for much more general spaces defined with the help of an operator acting from some function space to the cone of nonnegative nondecreasing functions on $(0,\infty)$. It is also shown how the classical interpolation theorems due to Stein–Weiss, Peetre, Calderón, Gilbert, Lizorkin, Freitag and some of their new variants can be derived from this theorem. 
@article{TM_2014_284_a5,
     author = {V. I. Burenkov and E. D. Nursultanov and D. K. Chigambayeva},
     title = {Description of the interpolation spaces for a~pair of local {Morrey-type} spaces and their generalizations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {105--137},
     publisher = {mathdoc},
     volume = {284},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_284_a5/}
}
TY  - JOUR
AU  - V. I. Burenkov
AU  - E. D. Nursultanov
AU  - D. K. Chigambayeva
TI  - Description of the interpolation spaces for a~pair of local Morrey-type spaces and their generalizations
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2014
SP  - 105
EP  - 137
VL  - 284
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2014_284_a5/
LA  - ru
ID  - TM_2014_284_a5
ER  - 
%0 Journal Article
%A V. I. Burenkov
%A E. D. Nursultanov
%A D. K. Chigambayeva
%T Description of the interpolation spaces for a~pair of local Morrey-type spaces and their generalizations
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2014
%P 105-137
%V 284
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2014_284_a5/
%G ru
%F TM_2014_284_a5
V. I. Burenkov; E. D. Nursultanov; D. K. Chigambayeva. Description of the interpolation spaces for a~pair of local Morrey-type spaces and their generalizations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces and related problems of analysis, Tome 284 (2014), pp. 105-137. http://geodesic.mathdoc.fr/item/TM_2014_284_a5/