Li, Tie; Jiang, Yinsheng; Zhou, Jiang Boundedness of parameterized Littlewood-Paley operators with non-doubling measures on Morrey spaces. (English) Zbl 1313.42070 J. Xinjiang Univ., Nat. Sci. 31, No. 1, 52-56 (2014). Summary: Let \(\mu\) be a non-negative Radon measure on \(\mathbb R^d\) which only satisfies the following growth condition that there exists a positive constant \(C\) such that \(\mu(B(x, r))\leq Cr^n\) for all \(x\in \mathbb R^d\), \(r>0\) and some fixed \(n\in (0, d]\). We prove that for suitable indexes \(\rho\) and \(\lambda\) the parameterized \(g^*_\lambda\) function \({\mathcal M}^{*,\rho}_\lambda\) and \({\mathcal M}^\rho\) are bounded on \(M^p_q(k,\mu)\) spaces. MSC: 42B25 Maximal functions, Littlewood-Paley theory Keywords:non-doubling measures; Morrey space; parameterized Littlewood-Paley operators; parameterized Marcinkiewicz operators PDFBibTeX XMLCite \textit{T. Li} et al., J. Xinjiang Univ., Nat. Sci. 31, No. 1, 52--56 (2014; Zbl 1313.42070)