@article{c081af8624534979bf948b2512a5f3b5,
title = "Inversion of the Bessel potential operator in weighted variable Lebesgue spaces",
abstract = "We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting.",
keywords = "Approximative inverse operators, Bessel potentials, Variable exponent, Weighted spaces",
author = "Alexandre Almeida and Humberto Rafeiro",
note = "Funding Information: The authors would like to thank Professor S. Samko for some remarks to the paper. The first author is also grateful to Unidade de Investiga{\c c}{\~a}o “Matem{\'a}tica e Aplica{\c c}{\~o}es” of University of Aveiro for partial support. The second named author also acknowledges the financial support by Funda{\c c}{\~a}o para a Ci{\^e}ncia e Tecnologia (FCT) (Grant No. SFRH/BD/22977/2005), through Programa Operacional Ci{\^e}ncia e Inova{\c c}{\~a}o 2010 (POCI2010) of the Portuguese Government, co-financed by the European Community Fund FSE. Funding Information: Research supported by INTAS Grant No. 06-1000017-8792 through the project Variable Exponent Analysis. Corresponding author. E-mail addresses: jaralmeida@ua.pt (A. Almeida), hrafeiro@ualg.pt (H. Rafeiro).",
year = "2008",
month = apr,
day = "15",
doi = "10.1016/j.jmaa.2007.09.064",
language = "English",
volume = "340",
pages = "1336--1346",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",
}