Geodesic
Description of interpolation spaces for general local Morrey-type spaces
Eurasian mathematical journal, Tome 4 (2013) no. 1, pp. 46-53.

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We consider the real interpolation method and prove that for general local Morrey-type spaces, in the case when they have the same integrability parameter, the interpolation spaces are again general local Morrey-type spaces with appropriately chosen parameters. 
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V. I. Burenkov; D. K. Darbayeva; E. D. Nursultanov. Description of interpolation spaces for general local Morrey-type spaces. Eurasian mathematical journal, Tome 4 (2013) no. 1, pp. 46-53. http://geodesic.mathdoc.fr/item/EMJ_2013_4_1_a3/

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

[2] 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

[3] 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 | Zbl

[4] V. I. Burenkov, E. D. Nursultanov, “Description of interpolation spaces for local Morrey-type spaces”, Trudy Math. Inst. Steklov, 269, 2010, 46–56 | DOI | MR | Zbl

[5] V. I. Burenkov, D. K. Darbayeva, E. D. Nursultanov, “Description of interpolation spaces for the pair of local Morrey-type spaces and their generalizations”, Trudy Math. Inst. Steklov, 2013 (to appear)

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

[7] V. S. Guliyev, “Generalized weighted Morrey spaces and higher order commutators of sublinear operators”, Eurasian Mathematical Journal, 3:3 (2012), 33–61 | MR | Zbl

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

[9] P. G. Lemarié-Rieusset, “Multipliers and Morrey spaces”, Potential Analysis, 38 (2013), 741–752 | DOI | MR | Zbl

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

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

[12] M. A. Ragusa, “Operators in Morrey type spaces and applications”, Eurasian Mathematical Journal, 3:3 (2012), 94–109 | MR | Zbl

[13] A. Ruiz, L. Vega, “Corrigenda to “Unique continuation for Schrödinger operators” and a remark on interpolation on Morrey spaces”, Publ. Mat., Barc., 39 (1995), 405–411 | DOI | MR | Zbl

[14] W. Sickel, “Smoothness spaces related to Morrey spaces — a survey, I”, Eurasian Mathematical Journal, 3:3 (2012), 110–149 | MR | Zbl

[15] W. Sickel, “Smoothness spaces related to Morrey spaces — a survey, II”, Eurasian Mathematical Journal, 4:1 (2013), 82–124 | MR | Zbl

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

[17] T. V. Tararykova, “Comments on definitions of general local and global Morrey-type spaces”, Eurasian Mathematical Journal, 4:1 (2013), 125–134 | Zbl

[18] M. Taylor, “Analysis on Morrey spaces and applications to Navier–Stokes and other evolution equations”, Comm. Partial Differential Equations, 17 (1992), 1407–1456 | DOI | MR | Zbl