On Trudinger–Moser type inequalities involving Sobolev–Lorentz spaces

Abstract

Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness.

Equivalent Moser type inequalities inR2and the zero mass case

“…[5,29,33,34,17] and references therein. Further generalizations and closely related problems can be found in [12,11,23,32,52]. The first part of this work aims to better clarify the notion of criticality related to inequalities (1.2), (1.3) and (1.4) in connection with the parameter β.…”

“…[5,29,33,34,17] and references therein. Further generalizations and closely related problems can be found in [12,11,23,32,52].…”