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