Volume 29, Issue 3
A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces

Anal. Theory Appl., 29 (2013), pp. 221-233.

Published online: 2013-07

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• Abstract

Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted Hardy space. In this paper, by using the atomic decomposition of $H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators $T^\delta_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy spaces $WH^p_w(\mathbb R^n)$ for $0 < p < 1$ and $\delta=n/p-(n+1)/2$. This result is new even in the unweighted case.

• Keywords

Bochner-Riesz operator, weighted Hardy space, weighted weak Hardy space, $A_p$ weight, atomic decomposition.

42B15, 42B25, 42B30

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• RIS
• TXT
@Article{ATA-29-221, author = { and Hua Wang and and 21647 and and Hua Wang}, title = {A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {3}, pages = {221--233}, abstract = {

Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted Hardy space. In this paper, by using the atomic decomposition of $H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators $T^\delta_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy spaces $WH^p_w(\mathbb R^n)$ for $0 < p < 1$ and $\delta=n/p-(n+1)/2$. This result is new even in the unweighted case.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n3.3}, url = {http://global-sci.org/intro/article_detail/ata/5059.html} }
TY - JOUR T1 - A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces AU - Hua Wang , JO - Analysis in Theory and Applications VL - 3 SP - 221 EP - 233 PY - 2013 DA - 2013/07 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n3.3 UR - https://global-sci.org/intro/article_detail/ata/5059.html KW - Bochner-Riesz operator, weighted Hardy space, weighted weak Hardy space, $A_p$ weight, atomic decomposition. AB -

Let $w$ be a Muckenhoupt weight and $H^p_w(\mathbb R^n)$ be the weighted Hardy space. In this paper, by using the atomic decomposition of $H^p_w(\mathbb R^n)$, we will show that the Bochner-Riesz operators $T^\delta_R$ are bounded from $H^p_w(\mathbb R^n)$ to the weighted weak Hardy spaces $WH^p_w(\mathbb R^n)$ for $0 < p < 1$ and $\delta=n/p-(n+1)/2$. This result is new even in the unweighted case.

Hua Wang. (1970). A New Estimate for Bochner-Riesz Operators at the Critical Index on Weighted Hardy Spaces. Analysis in Theory and Applications. 29 (3). 221-233. doi:10.4208/ata.2013.v29.n3.3
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