Notes on the paper entitled ‘Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces’

摘要

The purpose of this note is to clarify the novelty of the paper entitled ‘Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces’ which was published in the J. Inequal. Appl. 2013:381, 2013 [1]. After this paper was published, the authors were informed of the references [2, 3, 4, 5], and [6], the results of which partly overlap with those of [1]. In the paper [1], the authors established the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces Hnpp,q(Rn); see Section 2 in [1] for the precise definition of Hnpp,q(Rn). The main theorem in [1] is stated as follows.