We derive weighted rearrangement estimates for a large class of area integrals. The main approach used earlier to study these questions is based on distribution function inequalities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-1, author = {A. K. Lerner}, title = {Rearrangement estimates of the area integrals}, journal = {Colloquium Mathematicae}, volume = {91}, year = {2002}, pages = {1-7}, zbl = {0987.31001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-1} }
A. K. Lerner. Rearrangement estimates of the area integrals. Colloquium Mathematicae, Tome 91 (2002) pp. 1-7. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-1/