Rubio de Francia extrapolation theorem in variable Lebesgue spaces for B_p(· ) weights

In this paper, we prove Rubio de Francia extrapolation results for pair of non-increasing functions with B_p(· ) weights. The case of B_∞ weights has also been proved. These results have been applied to obtain the extrapolation results in the framework of variable exponent Lebesgue space L^p(· )_w with Luxemburg norm. Also, an improved norm estimate for the boundedness of Hardy averaging operator on variable exponent Lebesgue space is given.