On a Weighted Adachi-Tanaka Type Trudinger-Moser Inequality in Nonradial Sobolev Spaces

摘要

In this article we establish a Trudinger-Moser inequality of Adachi-Tanaka type in nonradial weighted Sobolev spaces for functions defined on the whole R-N: The main tools used are the Besicovitch covering lemma and a Trudinger-Moser inequality on the whole space established by S. Adachi and K. Tanaka.