Interpolation theorems for nonlinear urysohn integral operators in general Morrey-type spaces
Eurasian mathematical journal, Tome 11 (2020) no. 4, pp. 87-94.

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

In this paper, we present new interpolation theorems for nonlinear Urysohn integral operators. In particular, interpolation theorems of Marcinkiewicz–Calderon type and Stein–Weiss–Peetre type are obtained.
@article{EMJ_2020_11_4_a7,
     author = {V. I. Burenkov and E. D. Nursultanov},
     title = {Interpolation theorems for nonlinear urysohn integral operators in general {Morrey-type} spaces},
     journal = {Eurasian mathematical journal},
     pages = {87--94},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2020_11_4_a7/}
}
TY  - JOUR
AU  - V. I. Burenkov
AU  - E. D. Nursultanov
TI  - Interpolation theorems for nonlinear urysohn integral operators in general Morrey-type spaces
JO  - Eurasian mathematical journal
PY  - 2020
SP  - 87
EP  - 94
VL  - 11
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2020_11_4_a7/
LA  - en
ID  - EMJ_2020_11_4_a7
ER  - 
%0 Journal Article
%A V. I. Burenkov
%A E. D. Nursultanov
%T Interpolation theorems for nonlinear urysohn integral operators in general Morrey-type spaces
%J Eurasian mathematical journal
%D 2020
%P 87-94
%V 11
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2020_11_4_a7/
%G en
%F EMJ_2020_11_4_a7
V. I. Burenkov; E. D. Nursultanov. Interpolation theorems for nonlinear urysohn integral operators in general Morrey-type spaces. Eurasian mathematical journal, Tome 11 (2020) no. 4, pp. 87-94. http://geodesic.mathdoc.fr/item/EMJ_2020_11_4_a7/

[1] T. U. Aubakirov, E. D. Nursultanov, “Spaces of processes, interpolation theorems”, Uspekhi Matem. Nauk, 61 (372):6 (2006), 181–182 (in Russian) | DOI | MR

[2] T. U. Aubakirov, E. D. Nursultanov, “Interpolation theorem for stochastic processes”, Eurasian Math. J., 1:1 (2010), 8–16 | MR | Zbl

[3] T. U. Aubakirov, E. D. Nursultanov, “Interpolation methods for stochastic processes spaces”, Abstr. Appl. Anal., 2013, 152043, 12 pp. | MR | Zbl

[4] O. Blasco, A. Ruiz, L. Vega, “Non interpolation in Morrey-Campanato and block spaces”, Ann. Scuola Norm. Super. Pisa, Classe di Scienze 4-e série, 28:1 (1999), 31–40 | MR | Zbl

[5] Russian Acad. Sci. Dokl. Math., 67 (2003) | MR | Zbl

[6] V. I. Burenkov, H. V. Guliyev, “Necessary and sufficient conditions for boundedness of the maximal operator in the local Morrey-type spaces”, Studia Mathematica, 163:2 (2004), 157–176 | DOI | MR | Zbl

[7] Russian Acad. Sci. Dokl. Math., 7 (2006) | MR

[8] V. I. Burenkov, H. V. Guliyev, V. S. Guliyev, “Necessary and sufficient conditions for boundedness of the fractional maximal operator in the local Morrey-type spaces”, J. Comput. Appl. Math., 208:1 (2007), 280–301 | DOI | MR | Zbl

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

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

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

[12] V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. Journal, 9:2 (2018), 82–88 | DOI | MR | Zbl

[13] V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem for Morreytype spaces and its corollaries”, Complex Var. Elliptic Equ., 65:1 (2020), 87–108 | DOI | MR | Zbl

[14] A. P. Calderon, “Spaces between $L_1$ and $L_\infty$ and the theorem of Marcinkiewicz”, Studia Math., 26 (1966), 273–299 | DOI | MR | Zbl

[15] A. Campanato, M. K. V. Murthy, “Una generalizzazione del teorema di Riesz-Thorin”, Ann. Scuola Norm. Super. Pisa, Classe di Scienze, 19 (1965), 87–100 | MR | Zbl

[16] A. G. Kostyuchenko, E. D. Nursultanov, “On integral operators in $L_p$-spaces”, Fund. Prikl. Matem., 5:2 (1999), 475–491 (in Russian) | MR | Zbl

[17] M. A. Krasnoselsky, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevsky, Integral operators in spaces of summable functions, Nauka, M., 1966 (in Russian) | MR

[18] P. G. Lemari'e-Rieusset, “The role of Morrey spaces in the study of Navier-Stokes and Euler equations”, Eurasian Math. Journal, 3:3 (2012), 62–93 | MR | Zbl

[19] P. G. Lemari'e-Rieusset, “Multipliers, Morrey spaces”, Potential Analysis, 38:3 (2013), 741–752 | DOI | MR | Zbl

[20] R. O. Oinarov, M. O. Otelbaev, “Criterion of contractivity of Urysohn operator”, Dokl. Ross. Akad. Nauk. Matematika, 255:6 (1980), 1316–1318 (in Russian) | MR | Zbl

[21] M. O. Otelbaev, G. A. Suvorchenkova, “Necessary and sufficient conditions for boundedness and continuity of a class of Urysohn operators”, Sibirsk. Matem. J., 20:2 (1979), 428–432 (in Russian) | MR | Zbl

[22] J. Peetre, “On the theory of $\mathcal{L}_{p,\lambda}$-spaces”, J. Func. Anal., 4 (1969), 71–87 | DOI | MR | Zbl

[23] J. Peetre, “A new approach in interpolation spaces”, Studia Math., 34 (1970), 23–42 | DOI | MR | Zbl

[24] A. Ruiz, L. Vega, “Corrigenda to “Unique...” and a remark on interpolation on Morrey spaces”, Publ. Mathematiques, 39 (1995), 405–411 | DOI | MR | Zbl

[25] G. Stampacchia, “$\mathcal{L}_{p,\lambda}$-spaces, interpolation”, Comm. Pure Appl. Math., 17 (1964), 293–306 | DOI | MR | Zbl

[26] E. M. Stein, G. Weiss, “Interpolation of operators with change of measures”, Trans. Amer. Math. Soc., 87 (1958), 159–172 | DOI | MR | Zbl