Anal. Theory Appl., 29 (2013), pp. 267-274.
Published online: 2013-07
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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 $L^1_{x^\alpha}(\mathbb{G}^n)$ to $L^q_{x^\beta}(\mathbb{G}^n)$ with the bound explicitly worked out and the similar result holds for $\mathcal{H}^\ast_n$.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/5062.html} }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 $L^1_{x^\alpha}(\mathbb{G}^n)$ to $L^q_{x^\beta}(\mathbb{G}^n)$ with the bound explicitly worked out and the similar result holds for $\mathcal{H}^\ast_n$.