Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-5, author = {C. J. Neugebauer}, title = {Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions}, journal = {Studia Mathematica}, volume = {192}, year = {2009}, pages = {51-60}, zbl = {1196.42019}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-5} }
C. J. Neugebauer. Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions. Studia Mathematica, Tome 192 (2009) pp. 51-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-5/