Geodesic
Sharp Extrapolation Theorems for Local Morrey Spaces
Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 82-97.

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

We show that the calculation of the sum of local Morrey spaces can be reduced to the calculation of the sum of sequence spaces that appear as parameters in the definition of local Morrey spaces. The presence of such a reduction allows us to obtain new extrapolation theorems for local Morrey spaces with sharp constants.
Keywords: Banach ideal space, local Morrey spaces, sum and intersection of spaces, extrapolation theorems. 
@article{TRSPY_2021_312_a3,
     author = {E. I. Berezhnoi},
     title = {Sharp {Extrapolation} {Theorems} for {Local} {Morrey} {Spaces}},
     journal = {Informatics and Automation},
     pages = {82--97},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a3/}
}
TY  - JOUR
AU  - E. I. Berezhnoi
TI  - Sharp Extrapolation Theorems for Local Morrey Spaces
JO  - Informatics and Automation
PY  - 2021
SP  - 82
EP  - 97
VL  - 312
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a3/
LA  - ru
ID  - TRSPY_2021_312_a3
ER  - 
%0 Journal Article
%A E. I. Berezhnoi
%T Sharp Extrapolation Theorems for Local Morrey Spaces
%J Informatics and Automation
%D 2021
%P 82-97
%V 312
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a3/
%G ru
%F TRSPY_2021_312_a3
E. I. Berezhnoi. Sharp Extrapolation Theorems for Local Morrey Spaces. Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 82-97. http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a3/

[1] E. I. Berezhnoi, “A sharp extrapolation theorem for Lorentz spaces”, Sib. Math. J., 54:3 (2013), 406–418 | DOI | MR | Zbl

[2] E. I. Berezhnoi, “Can Yano's extrapolation theorem be strengthened?”, Math. Notes, 49:2 (2015), 145–147 | MR | Zbl

[3] E. I. Berezhnoi, “A discrete version of local Morrey spaces”, Izv. Math., 81:1 (2017), 1–28 | DOI | MR | Zbl

[4] E. I. Berezhnoi, “Exact calculation of sums of the Lorentz spaces $\Lambda ^\alpha $ and applications”, Math. Notes, 104:5 (2018), 628–635 | DOI | MR | Zbl

[5] E. I. Berezhnoi, “Exact calculation of sums of cones in Lorentz spaces”, Funct. Anal. Appl., 52:2 (2018), 134–138 | DOI | MR | Zbl

[6] E. I. Berezhnoi, “Extremal extrapolation spaces”, Funct. Anal. Appl., 54:1 (2020), 1–6 | DOI | MR | Zbl

[7] E. I. Berezhnoi and A. A. Perfil'ev, “A sharp extrapolation theorem for operators”, Funct. Anal. Appl., 34:3 (2000), 211–213 | DOI | MR | Zbl

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

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

[10] V. I. Burenkov, E. D. Nursultanov, and D. K. Chigambayeva, “Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations”, Proc. Steklov Inst. Math., 284 (2014), 97–128 | DOI | MR | Zbl

[11] Carro M.J., “On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity”, Publ. Mat. Barc., Extra (2002), 27–37 | DOI | MR | Zbl

[12] Fiorenza A., Gupta B., Jain P., “The maximal theorem for weighted Grand Lebesgue spaces”, Stud. math., 188:2 (2008), 123–133 | DOI | MR | Zbl

[13] Fiorenza A., Karadzhov G.E., “Grand and small Lebesgue spaces and their analogs”, Z. Anal. Anwend., 23:4 (2004), 657–681 | DOI | MR | Zbl

[14] Iwaniec T., Sbordone C., “On the integrability of the Jacobian under minimal hypotheses”, Arch. Ration. Mech. Anal., 119:2 (1992), 129–143 | DOI | MR | Zbl

[15] Jawerth B., Milman M., Extrapolation theory with applications, Mem. Amer. Math. Soc., 89, no. 440, Amer. Math. Soc., Providence, RI, 1991 | MR

[16] Karadzhov G.E., Milman M., “Extrapolation theory: New results and applications”, J. Approx. Theory, 133:1 (2005), 38–99 | DOI | MR | Zbl

[17] S. G. Kreĭn, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators, Am. Math. Soc, Providence, RI, 1982 | MR | Zbl

[18] Kufner A., Maligranda L., Persson L.-E., The Hardy inequality: About its history and some related results, Vydavatelský Servis, Pilsen, 2007 | MR | Zbl

[19] Lindenstrauss J., Tzafriri L., Classical Banach spaces. I: Sequence spaces; II: Function spaces, Ergebn. Math. Grenzgeb., 92, 97, Springer, Berlin, 1977, 1979 | MR

[20] Milman M., Extrapolation and optimal decompositions: With applications to analysis, Lect. Nothes Math., 1580, Springer, Berlin, 1994 | DOI | MR | Zbl

[21] Morrey C.B., \textup {Jr.}, “On the solutions of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43:1 (1938), 126–166 | DOI | MR

[22] Sbordone C., “Grand Sobolev spaces and their application to variational problems”, Matematiche, 51:2 (1996), 335–347 | MR | Zbl

[23] Yano S., “Notes on Fourier analysis. XXIX: An extrapolation theorem”, J. Math. Soc. Japan, 3:2 (1951), 296–305 | DOI | MR | Zbl

[24] A. Zygmund, Trigonometric Series, v. 2, Univ. Press, Cambridge, 1959 | MR | Zbl