TY - JOUR
T1 - Endpoint Estimates for Hardy Operatorâ€™s Conjugate Operator with Power Weight on $n$-Dimensional Space
JO - Analysis in Theory and Applications
VL - 3
SP - 267
EP - 274
PY - 2013
DA - 2013/07
SN - 29
DO - http://doi.org/10.4208/ata.2013.v29.n3.6
UR - https://global-sci.org/intro/article_detail/ata/5062.html
KW - Conjugate operator, power weight, endpoint estimate.
AB - 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 $\mathcal{H}^\ast_n$.