Parametric Marcinkiewicz integral operator on generalized Orlicz-Morrey spaces. (English) Zbl 1513.42035
Summary: In this paper we study the boundedness of the parametric Marcinkiewicz integral operator \(\mu_\Omega^\rho\) on generalized Orlicz-Morrey spaces \(M_{\Phi,\varphi}\). We find the sufficient conditions on the pair \((\varphi_1,\varphi_2, \Phi)\) which ensure the boundedness of the operators \(\mu_\Omega^\rho\) from one generalized Orlicz-Morrey space \(M_{\Phi,\varphi_1}\) to \(M_{\Phi,\varphi_2}\). As an application of the above result, the boundedness of the Marcinkiewicz operator associated with Schrödinger operator \(\mu_j^L\) on generalized Orlicz-Morrey spaces is also obtained.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42B35 | Function spaces arising in harmonic analysis |
| 35J10 | Schrödinger operator, Schrödinger equation |
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