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

Abstract

*Correspondence: wadade@se.kanazawa-u.ac.jp 3Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan Full list of author information is available at the end of the article 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. :,  []. After this paper was published, the authors were informed of the references [–], and [], the results of which partly overlap with those of []. In the paper [], the authors established the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces H n p p,q(R); see Section  in [] for the precise definition of H n p p,q(R). The main theorem in [] is stated as follows. Theorem A [, Theorem .] Let n ∈ N,  < p <∞,  < q≤∞ and  < α,β <∞. Then the inequality (∫