We derive inequalities of Gagliardo-Nirenberg type in weighted Orlicz spaces on ℝⁿ, for maximal functions of derivatives and for the derivatives themselves. This is done by an application of pointwise interpolation inequalities obtained previously by the first author and of Muckenhoupt-Bloom-Kerman-type theorems for maximal functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-1-4,
author = {Agnieszka Ka\l amajska and Katarzyna Pietruska-Pa\l uba},
title = {Gagliardo-Nirenberg inequalities in weighted Orlicz spaces},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {49-71},
zbl = {1093.26011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-1-4}
}
Agnieszka Kałamajska; Katarzyna Pietruska-Pałuba. Gagliardo-Nirenberg inequalities in weighted Orlicz spaces. Studia Mathematica, Tome 173 (2006) pp. 49-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-1-4/