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 - <p style="text-align: justify;">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 $1 &lt; q\leq \alpha &lt; p\leq \infty$.</p>