We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-1, author = {Amiran Gogatishvili and Pekka Koskela}, title = {A non-doubling Trudinger inequality}, journal = {Studia Mathematica}, volume = {166}, year = {2005}, pages = {113-119}, zbl = {1091.46019}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-1} }
Amiran Gogatishvili; Pekka Koskela. A non-doubling Trudinger inequality. Studia Mathematica, Tome 166 (2005) pp. 113-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-1/