Boundedness of Littlewood-Paley operators with variable kernel on the weighted Herz-Morrey spaces with variable exponent. (English) Zbl 1449.43002
Summary: Let \(\Omega\in L^\infty(\mathbb{R}^n)\times L^2(S^{n-1})\) be a homogeneous function of degree zero. In this article, we obtain some boundedness of the parameterized Littlewood-Paley operators with variable kernels on weighted Herz-Morrey spaces with variable exponent. As a supplement, the boundedness of fractional integral operators with variable kernel is also obtained on these spaces.
MSC:
43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
43A85 | Harmonic analysis on homogeneous spaces |