A sublinear Sobolev inequality forp-superharmonic functions

Document Type

Article

Publication Date

1-1-2017

Abstract

We establish a “sublinear” Sobolev inequality of the form (Formula Presented) for all global p-superharmonic (1 < p < 2) functions u in ℝn, n ≥ 2, with infℝn u = 0 and p − 1 < q < 1. The same result also holds for the class of A-superharmonic functions. More general sublinear trace inequalities, where Lebesgue measure is replaced by a general measure, are also considered.

Publication Source (Journal or Book title)

Proceedings of the American Mathematical Society

First Page

327

Last Page

334

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