Hardy’s inequality in a limiting case on general bounded domains

In this paper, we study Hardy’s inequality in a limiting case: [Formula: see text] for functions [Formula: see text], where [Formula: see text] is a bounded domain in [Formula: see text] with [Formula: see text]. We study the attainability of the best constant [Formula: see text] in several cases. We provide sufficient conditions that assure [Formula: see text] and [Formula: see text] is attained, here [Formula: see text] is the [Formula: see text]-dimensional ball with center the origin and radius [Formula: see text]. Also, we provide an example of [Formula: see text] such that [Formula: see text] and [Formula: see text] is not attained.