Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures

Osvaldo Gorosito; Gladis Pradolini; Oscar Salinas

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 1007-1023
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Gorosito, Osvaldo, Pradolini, Gladis, and Salinas, Oscar. "Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures." Czechoslovak Mathematical Journal 60.4 (2010): 1007-1023. <http://eudml.org/doc/196362>.

@article{Gorosito2010,
abstract = {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.},
author = {Gorosito, Osvaldo, Pradolini, Gladis, Salinas, Oscar},
journal = {Czechoslovak Mathematical Journal},
keywords = {variable exponent; weighted spaces; non doubling measures; variable exponent; weighted space; non doubling measures},
language = {eng},
number = {4},
pages = {1007-1023},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures},
url = {http://eudml.org/doc/196362},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Gorosito, Osvaldo
AU - Pradolini, Gladis
AU - Salinas, Oscar
TI - Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 1007
EP - 1023
AB - 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.
LA - eng
KW - variable exponent; weighted spaces; non doubling measures; variable exponent; weighted space; non doubling measures
UR - http://eudml.org/doc/196362
ER -

References

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  1. Almeida, A., Samko, S., 10.1007/s00009-009-0006-7, Mediterr. J. Math. 6 (2009), 215-232. (2009) Zbl1182.43011MR2516251DOI10.1007/s00009-009-0006-7
  2. Capone, C., Cruz-Uribe, D., Fiorenza, A., 10.4171/RMI/511, Rev. Mat. Iberoam. 23 (2007), 743-770. (2007) MR2414490DOI10.4171/RMI/511
  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. (2003) MR1976842
  4. Diening, L., Maximal function on generalized Lebesgue spaces L p ( · ) , Math. Inequal. Appl. 7 (2004), 245-254. (2004) MR2057643
  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. (2001) MR1871355
  6. Harjulehto, P., Hästö, P., Latvala, V., 10.1007/s00209-006-0960-8, Math. Z. 254 (2006), 591-609. (2006) MR2244368DOI10.1007/s00209-006-0960-8
  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. (2004) MR2126796
  8. Kokilashvili, V., Samko, S., 10.4171/RMI/398, Rev. Mat. Iberoam. 20 (2004), 493-515. (2004) MR2073129DOI10.4171/RMI/398
  9. Kováčik, O., Rákosník, J., On spaces L p ( x ) and W k , p ( x ) , Czechoslovak Math. J. 41(116) (1991), 592-618. (1991) MR1134951
  10. Musielak, J., Orlicz spaces and Modular spaces. Lecture Notes in Math. Vol. 1034, Springer Berlin (1983). (1983) MR0724434
  11. Muckenhoupt, B., Wheeden, R. L., 10.1090/S0002-9947-1974-0340523-6, Trans. Am. Math. Soc. 192 (1974), 261-274. (1974) Zbl0289.26010MR0340523DOI10.1090/S0002-9947-1974-0340523-6
  12. Pick, L., Růžička, M., 10.1016/S0723-0869(01)80023-2, Expo. Math. 4 (2001), 369-372. (2001) MR1876258DOI10.1016/S0723-0869(01)80023-2
  13. Růžička, M., 10.1007/BFb0104030, Springer Berlin (2000). (2000) MR1810360DOI10.1007/BFb0104030
  14. Samko, S., Hardy-Littlewood-Stein-Weiss inequality in the Lebesgue spaces with variable exponent, Fract. Calc. Appl. Anal. 6 (2003), 421-440. (2003) Zbl1093.46015MR2044308
  15. Welland, G. V., 10.1090/S0002-9939-1975-0369641-X, Proc. Am. Math. Soc. 51 (1975), 143-148. (1975) Zbl0306.26007MR0369641DOI10.1090/S0002-9939-1975-0369641-X

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