Geodesic
Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1007-1023.

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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.
Classification : 42B25
Keywords: variable exponent; weighted spaces; non doubling measures 
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     title = {Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1007--1023},
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Gorosito, Osvaldo; Pradolini, Gladis; Salinas, Oscar. Boundedness of fractional operators in weighted variable exponent spaces with non doubling measures. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1007-1023. http://geodesic.mathdoc.fr/item/CMJ_2010__60_4_a8/