Volume 29, Issue 2
The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (Lq,Lp)α(Rn) Spaces

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 $1 < q\leq \alpha < p\leq \infty$.
• Keywords

Littlewood-Paley operator weighted amalgam space rough kernel Ap weight

42B25 42B20

@Article{ATA-29-135, author = {X. M.Wei and S. P. Tao}, title = {The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (Lq,Lp)α(Rn) 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 (Lq,Lp)α(Rn) Spaces AU - X. M.Wei & S. P. Tao 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 KW - weighted amalgam space KW - rough kernel KW - Ap 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 $1 < q\leq \alpha < p\leq \infty$.