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Title: Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures (English)
Author: Gorosito, Osvaldo
Author: Pradolini, Gladis
Author: Salinas, Oscar
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 4
Year: 2010
Pages: 1007-1023
Summary lang: English
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Category: math
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Summary: In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator. (English)
Keyword: variable exponent
Keyword: weighted spaces
Keyword: non doubling measures
MSC: 42B25
idZBL: Zbl 1224.42060
idMR: MR2738962
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Date available: 2010-11-20T13:56:09Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/140799
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Reference: [1] Almeida, A., Samko, S.: Fractional and hypersingular operators in variable exponent spaces on metric measure spaces.Mediterr. J. Math. 6 (2009), 215-232. Zbl 1182.43011, MR 2516251, 10.1007/s00009-009-0006-7
Reference: [2] Capone, C., Cruz-Uribe, D., Fiorenza, A.: The fractional maximal operator and fractional integrals on variable $L^p$ spaces.Rev. Mat. Iberoam. 23 (2007), 743-770. MR 2414490, 10.4171/RMI/511
Reference: [3] Cruz-Uribe, D., Fiorenza, A., Neugebauer, C. J.: The maximal function on variable $L^p$ spaces.Ann. Acad. Sci. Fenn., Math. 28 (2003), 223-238. MR 1976842
Reference: [4] Diening, L.: Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$.Math. Inequal. Appl. 7 (2004), 245-254. MR 2057643
Reference: [5] Cuerva, J. García, Martell, J. M.: Two-weight norm inequalities for maximal operators and fractional integrals on non-homogeneous spaces.Indiana Univ. Math. J. 50 (2001), 1241-1280. MR 1871355
Reference: [6] Harjulehto, P., Hästö, P., Latvala, V.: Sobolev embeddings in metric measure spaces with variable dimension.Math. Z. 254 (2006), 591-609. MR 2244368, 10.1007/s00209-006-0960-8
Reference: [7] Harjulehto, P., Hästö, P., Pere, M.: Variable exponent Lebesgue spaces on metric spaces: The Hardy-Littlewood maximal operator.Real Anal. Exch. 30 (2004/2005), 87-104. MR 2126796
Reference: [8] Kokilashvili, V., Samko, S.: Maximal and fractional operators in weighted $L^{p(x)}$ spaces.Rev. Mat. Iberoam. 20 (2004), 493-515. MR 2073129, 10.4171/RMI/398
Reference: [9] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$.Czechoslovak Math. J. 41(116) (1991), 592-618. MR 1134951
Reference: [10] Musielak, J.: Orlicz spaces and Modular spaces. Lecture Notes in Math. Vol. 1034.Springer Berlin (1983). MR 0724434
Reference: [11] Muckenhoupt, B., Wheeden, R. L.: Weighted norm inequalities for fractional integrals.Trans. Am. Math. Soc. 192 (1974), 261-274. Zbl 0289.26010, MR 0340523, 10.1090/S0002-9947-1974-0340523-6
Reference: [12] Pick, L., Růžička, M.: An example of a space $L^{p(x)}$ on which the Hardy-Littlewood maximal operator is not bounded.Expo. Math. 4 (2001), 369-372. MR 1876258, 10.1016/S0723-0869(01)80023-2
Reference: [13] Růžička, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Math. Vol. 1748.Springer Berlin (2000). MR 1810360, 10.1007/BFb0104030
Reference: [14] Samko, S.: Hardy-Littlewood-Stein-Weiss inequality in the Lebesgue spaces with variable exponent.Fract. Calc. Appl. Anal. 6 (2003), 421-440. Zbl 1093.46015, MR 2044308
Reference: [15] Welland, G. V.: Weighted norm inequalities for fractional integrals.Proc. Am. Math. Soc. 51 (1975), 143-148. Zbl 0306.26007, MR 0369641, 10.1090/S0002-9939-1975-0369641-X
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