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Volume 29, Issue 3
Endpoint Estimates for Hardy Operator’s Conjugate Operator with Power Weight on $n$-Dimensional Space

X. Nie, S. Wang & D. Yan

Anal. Theory Appl., 29 (2013), pp. 267-274.

Published online: 2013-07

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  • Abstract

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 $\mathcal{H}^\ast_n$.

  • AMS Subject Headings

42B20, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-29-267, author = {X. Nie, S. Wang and D. Yan}, title = {Endpoint Estimates for Hardy Operator’s Conjugate Operator with Power Weight on $n$-Dimensional Space}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {3}, pages = {267--274}, abstract = {

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} }
TY - JOUR T1 - Endpoint Estimates for Hardy Operator’s Conjugate Operator with Power Weight on $n$-Dimensional Space AU - X. Nie, S. Wang & D. Yan 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 $\mathcal{H}^\ast_n$.

X. Nie, S. Wang and D. Yan. (2013). Endpoint Estimates for Hardy Operator’s Conjugate Operator with Power Weight on $n$-Dimensional Space. Analysis in Theory and Applications. 29 (3). 267-274. doi:10.4208/ata.2013.v29.n3.6
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