Abstract
We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type Lu:=ârâΞ(rα|uâČ(r)|ÎČuâČ(r))âČ, where Ξ,ÎČâ„0 and α>0, are constants satisfying some existence conditions. It is worth emphasizing that these operators generalize the p-Laplacian and k-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted PĂłlya-Szegö principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.
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