Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces
Kokilashvili, Vakhtang ; Samko, Stefan
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 493-515 / Harvested from Project Euclid
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We study the boundedness of the maximal operator, potential type operators and operators with fixed singularity (of Hardy and Hankel type) in the spaces $L^{p(\cdot)}(\rho,\Omega)$ over a bounded open set in $\mathbb{R}^n$ with a power weight $\rho(x)=|x-x_0|^\gamma$, $x_0\in \overline{\Omega}$, and an exponent $p(x)$ satisfying the Dini-Lipschitz condition.
Publié le : 2004-06-14
Classification:  maximal functions,  weighted Lebesgue spaces,  variable exponent,  potential operators,  integral operators with fixed singularity,  42B25,  47B38 
@article{1087482024,
     author = {Kokilashvili, Vakhtang and Samko, Stefan},
     title = {Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 493-515},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087482024}
}

Kokilashvili, Vakhtang; Samko, Stefan. Maximal and Fractional Operators in Weighted $L^{p(x)}$ Spaces. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  493-515. http://gdmltest.u-ga.fr/item/1087482024/