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Volume 29, Issue 2
The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q, L^p)^{\alpha}(\mathbf{R}^n)$ Spaces

X. M. Wei & S. P. Tao

Anal. Theory Appl., 29 (2013), pp. 135-148.

Published online: 2013-06

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  • Abstract

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral $\mu_{\Omega,s}$ and Littlewood-Paley functions $\mu_{\Omega}$ and $\mu^{*}_{\lambda}$ on the weighted amalgam spaces $(L^{q}_\omega,L^{p})^{\alpha}(\mathbf{R}^{n})$ as $1 < q\leq \alpha < p\leq \infty$.

  • AMS Subject Headings

42B25, 42B20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-29-135, author = {X. M. Wei , and Tao , S. P.}, title = {The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q, L^p)^{\alpha}(\mathbf{R}^n)$ Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {2}, pages = {135--148}, abstract = {

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral $\mu_{\Omega,s}$ and Littlewood-Paley functions $\mu_{\Omega}$ and $\mu^{*}_{\lambda}$ on the weighted amalgam spaces $(L^{q}_\omega,L^{p})^{\alpha}(\mathbf{R}^{n})$ as $1 < q\leq \alpha < p\leq \infty$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n2.5}, url = {http://global-sci.org/intro/article_detail/ata/4522.html} }
TY - JOUR T1 - The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q, L^p)^{\alpha}(\mathbf{R}^n)$ Spaces AU - X. M. Wei , AU - Tao , S. P. JO - Analysis in Theory and Applications VL - 2 SP - 135 EP - 148 PY - 2013 DA - 2013/06 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n2.5 UR - https://global-sci.org/intro/article_detail/ata/4522.html KW - Littlewood-Paley operator, weighted amalgam space, rough kernel, $A_p$ weight. AB -

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral $\mu_{\Omega,s}$ and Littlewood-Paley functions $\mu_{\Omega}$ and $\mu^{*}_{\lambda}$ on the weighted amalgam spaces $(L^{q}_\omega,L^{p})^{\alpha}(\mathbf{R}^{n})$ as $1 < q\leq \alpha < p\leq \infty$.

X. M. Wei & S. P. Tao. (1970). The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q, L^p)^{\alpha}(\mathbf{R}^n)$ Spaces. Analysis in Theory and Applications. 29 (2). 135-148. doi:10.4208/ata.2013.v29.n2.5
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