The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q, L^p)^{α}(R^n)$ Spaces (Analysis in Theory and Applications, 2013)
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 $μ_{Ω,s}$ and Littlewood-Paley functions $μ_{Ω}$ and $μ^{*}_{λ}$ on the weighted amalgam spaces $(L^{q}_ω,L^{p})^{α}(R^{n})$ as $1 < q≤ α < p≤ ∞$.
Keywords: Littlewood-Paley operator; weighted amalgam space; rough kernel; $A_p$ weight.