Boundedness of the parametric Littlewood-Paley operators on grand Herz-Morrey spaces with variable exponents

Abstract:

      We prove the boundedness of the parametric Lusin""s $S$ function $\mu^{\varrho}_S(f)$ and Littlewood-Paley""s $g^\ast_\lambda$-funtion $\mu^{\ast, \varrho}_\lambda(f)$ on grand Herz-Morrey spaces with variable exponents. Additionally, we establish the boundedness of higher-order commutators of $\mu^{\varrho}_S$ and $\mu^{\ast, \varrho}_\lambda$ with $BMO$ functions applying some properties of variable exponents and generalized BMO norms.