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Boundedness of parameterized Littlewood-Paley operators with non-doubling measures on Morrey spaces. (English) Zbl 1313.42070

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
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