Endpoint Estimates for Hardy Operator’s Conjugate Operator with Power Weight on $n$-Dimensional Space (Analysis in Theory and Applications, 2013)
In this paper, we establish two integral inequalities for Hardy operator's conjugate operator at the endpoint on $n$-dimensional space. The operator $H^*_n$ is bounded from $L^1_{x^α}(\mathbb{G}^n)$ to $L^q_{x^β}(\mathbb{G}^n)$ with the bound explicitly worked out and the similar result holds for $\mathcal{H}^*_n$.