|Title||Higher order Sobolev trace inequalities on balls revisited|
|Publication Type||Journal Article|
|Year of Publication||2020|
|Authors||Ngô, QAnh, Nguyen, VHoang, Phan, QHung|
|Journal||Journal of Functional Analysis|
|Keywords||Beckner inequality, Gaussian hypergeometric function, Higher order fractional Laplacian, Lebedev–Milin inequality, Sobolev trace inequality|
Inspired by a recent sharp Sobolev trace inequality of order four on the balls Bn+1 found by Ache and Chang (2017) , we propose a different approach to reprove Ache–Chang's trace inequality. To further illustrate this approach, we reprove the classical Sobolev trace inequality of order two on Bn+1 and provide sharp Sobolev trace inequalities of orders six and eight on Bn+1. To obtain all these inequalities up to order eight, and possibly more, we first establish higher order sharp Sobolev trace inequalities on R+n+1, then directly transferring them to the ball via a conformal change. As the limiting case of the Sobolev trace inequalities, Lebedev–Milin type inequalities of order up to eight are also considered.