Littlewood-Paley Operators on Spaces with Variable Exponent on Homogeneous Groups

Abstract

In this paper, on homogeneous groups, we study the Littlewood-Paley operators in variable exponent spaces. First, we prove that the weighted Littlewood-Paley operators are controlled by the weighted Hardy-Littlewood maximal function, and obtain the vector-valued inequalities of the Littlewood-Paley operators, including the Lusin function, Littlewood-Paley g function and $$g_\lambda ^*$$ function. Second, we prove the boundedness of multilinear Littlewood-Paley $$g_{\psi, \lambda}^*$$ function.