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Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. (English) Zbl 1205.26014

The author shows the boundedness of modified maximal operators and potentials with a variable parameter in variable exponent Morrey spaces with non-doubling measure. Also, Hölder continuity properties for fractional integrals of functions in Morrey spaces are investigated.

MSC:

26A33 Fractional derivatives and integrals
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B35 Function spaces arising in harmonic analysis
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[1] DOI: 10.1215/S0012-7094-75-04265-9 · Zbl 0336.46038
[2] Chiarenza F, Rend. Math. 7 pp 273– (1987)
[3] DOI: 10.1016/0022-1236(69)90022-6 · Zbl 0175.42602
[4] DOI: 10.1007/s10114-005-0660-z · Zbl 1129.42403
[5] Eridani A, Expo. Math. 27 pp 227– (2009)
[6] DOI: 10.1016/j.jmaa.2008.09.021 · Zbl 1155.42005
[7] DOI: 10.4064/sm163-2-4 · Zbl 1044.42015
[8] Burenkov IV, (Russian) Doklady Akademii Nauk 412 pp 585– (2007)
[9] Edmunds D, J. Funct. Spaces Appl. 2 pp 55– (2004)
[10] Harjulehto P, Real Anal. Exchange. 30 pp 87– (2004)
[11] Kokilashvili V, Proc. A. Razmadze Math. Inst. 144 pp 137– (2007)
[12] Kokilashvili V, Proc. A. Razmadze Math. Inst. 145 pp 109– (2007)
[13] Kokilashvili V, Nonlinear Analysis, Function Spaces and Applications IV (Roudnice nad Labem, 1990), Teubner-Textezur Mathematik 119 pp 86– (1990)
[14] Kokilashvili V, Frac. Calc. Appl. Anal. 4 pp 1– (2001)
[15] DOI: 10.4171/ZAA/1272
[16] Sawano Y, Hokkaido Math. J. 34 pp 435– (2005)
[17] Edmunds DE, Bounded and Compact Integral Operators, Mathematics and Its Applications 543 (2002)
[18] DOI: 10.4064/sm162-3-5 · Zbl 1045.42006
[19] Kováčik O, Czech. Math. J. 41 pp 592– (1991)
[20] Kokilashvili V, Rev. Mat. Iberoamericana 20 pp 493– (2004)
[21] DOI: 10.1080/10652469808819191 · Zbl 0934.46032
[22] Sharapudinov II, Mat. Zametki 26 pp 613– (1979)
[23] Cruz-Uribe D, Ann. Acad. Sci. Fenn. Math. 28 pp 223– (2003)
[24] Cruz-Uribe SFO D, Ann Acad. Sci. Fenn. Math. 31 pp 239– (2006)
[25] Diening L, Math. Inequal. Appl. 7 pp 245– (2004)
[26] DOI: 10.1002/mana.200310157 · Zbl 1065.46024
[27] DOI: 10.4171/ZAA/1178 · Zbl 1040.42013
[28] DOI: 10.1080/10652469808819204 · Zbl 1023.31009
[29] Kokilashvili V, Armenian J. Math. 1 pp 18– (2008)
[30] Almeida A, Georgian Math. J. 15 pp 195– (2008)
[31] DOI: 10.2969/jmsj/06020583 · Zbl 1161.46305
[32] DOI: 10.1090/S0002-9939-1972-0312232-4
[33] DOI: 10.1007/BF02257475 · Zbl 0820.26004
[34] DOI: 10.1155/S0161171295001001 · Zbl 0838.26005
[35] DOI: 10.4171/ZAA/1317 · Zbl 1131.46022
[36] Mizuta Y, Math. Inequal. Appl. (2009)
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