Geodesic
Calculation of the Calder\'on--Lozanovskii construction for a couple of local Morrey spaces
Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 21-34.

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

The calculation of the Calderón–Lozanovskii construction for a couple of local Morrey spaces is reduced to the calculation of the Calderón–Lozanovskii construction for two couples of ideal spaces of functions and sequences, that are the parameters in the definition of local Morrey spaces. These results allows us to obtain new interpolation theorems for operators on local Morrey spaces. 
@article{EMJ_2020_11_3_a1,
     author = {E. I. Berezhnoi},
     title = {Calculation of the {Calder\'on--Lozanovskii} construction for a couple of local {Morrey} spaces},
     journal = {Eurasian mathematical journal},
     pages = {21--34},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a1/}
}
TY  - JOUR
AU  - E. I. Berezhnoi
TI  - Calculation of the Calder\'on--Lozanovskii construction for a couple of local Morrey spaces
JO  - Eurasian mathematical journal
PY  - 2020
SP  - 21
EP  - 34
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a1/
LA  - en
ID  - EMJ_2020_11_3_a1
ER  - 
%0 Journal Article
%A E. I. Berezhnoi
%T Calculation of the Calder\'on--Lozanovskii construction for a couple of local Morrey spaces
%J Eurasian mathematical journal
%D 2020
%P 21-34
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a1/
%G en
%F EMJ_2020_11_3_a1
E. I. Berezhnoi. Calculation of the Calder\'on--Lozanovskii construction for a couple of local Morrey spaces. Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 21-34. http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a1/

[1] Izvestiya: Mathematics, 81:1 (2017), 1–28 | DOI | DOI | MR | Zbl

[2] E. I. Berezhnoi, “Interpolation of positive operators in the spaces $\varphi(X_0, X_1)$”, Qualitative and Approximate Methods for the Investigation of Operator Equations, Yaroslav. Gos. Univ., Yaroslavl, 1981, 3–12 (in Russian) | MR

[3] Soviet Math. (Iz. VUZ), 26:2 (1982), 107–111 | MR

[4] Functional Analysis and its Applications, 18:1 (1984), 48–50 | DOI | MR

[5] E. I. Berezhnoi, L. Maligranda, “Representation of Banach spaces and ideal factorization of operators”, Canad. J. Math., 57:5 (2005), 897–940 | DOI | MR | Zbl

[6] O. Blasco, A. Ruiz, L. Vega, “Non interpolation in Morrey-Companato and block spaces”, Ann. Scuola Norm. Super Pisa, 28:1 (1999), 31–40 | MR | Zbl

[7] Yu. A. Brudnyi, N. Ya. Krugljak, Interpolation functors and interpolation spaces, North-Holland, Amsterdam, 1991 | MR | Zbl

[8] V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Mathematical Journal, 3:3 (2012), 11–32 | MR | Zbl

[9] V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Mathematical Journal, 4:1 (2013), 21–45 | MR | Zbl

[10] V. I. Burenkov, D. K. Darbaeva, E. D. Nursultanov, “Description of interpolation spaces for general local Morreytype spaces”, Eurasian Mathematical Journal, 4:1 (2013), 46–53 | MR | Zbl

[11] Proceedings Steklov Inst. Math., 269 (2010), 46–56 | DOI | MR | Zbl

[12] Proceedings Steklov Inst. Math., 284 (2014), 97–128 | DOI | MR | Zbl

[13] Sb. Perevodov Matematika, 9:3 (1965), 56–129 | DOI | MR | Zbl

[14] J. Gustavsson, J. Peetre, “Interpolation of Orlicz spaces”, Studia Math., 60:1 (1977), 33–59 | DOI | MR | Zbl

[15] Pergamon Press, Oxford-Elmsford, New York, 1982 | MR | Zbl

[16] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of linear operators, American Mathematical Society, Providence, 1982 | MR

[17] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces, v. I, Sequence spaces, Springer-Verlag, Berlin–Heidelberg–New-York, 1977 | MR | Zbl

[18] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces, v. II, Function spaces, Springer-Verlag, Berlin–Heidelberg–New-York, 1979 | MR | Zbl

[19] G. Ya. Lozanovskii, “On some Banach lattices IV”, Siberian Math. J., 14 (1973), 97–108 | DOI | MR | Zbl

[20] L. Maligranda, Orlicz spaces, interpolation, Seminars in Math., 5, Univ. of Campinas, Campinas SP, Brazil, 1989 | MR | Zbl

[21] C. B. Morrey, “On the solution of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43 (1938), 126–166 | DOI | MR

[22] V. I. Ovchinnikov, “The methods of orbits in interpolation theory”, Math. Reports, 1:2 (1984), 349–516 | MR

[23] A. Ruiz, L. Vega, “Corrigendato “Unique continuation for Schrödinger operators” and remark on interpolation in Morrey spaces”, Publ. Math. Barc., 39 (1995), 405–411 | DOI | MR | Zbl