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The weighted Morrey type estimates for multilinear square function. (Chinese. English summary) Zbl 1389.42025

Summary: The continuity of a class of multilinear square function is studied and a binary decomposition technique is used to obtain the boundness of multilinear square function \(T\) on weighted Morrey spaces. That is, the \({L^{p1, \kappa}}\left( {{\omega_1}} \right) \times \cdots \times {L^{{p_m}, \kappa}}\left( {{\omega_m}} \right) \to {L^{p, \kappa}}\left( {{\nu_{\overrightarrow \omega}}} \right)\) estimate of \(T\) on each \({p_i} > 1\) and weak type \({L^{p1, \kappa}}\left( {{\omega_1}} \right) \times \cdots \times {L^{{p_m}, \kappa}}\left( {{\omega_m}} \right) \to {WL^{p, \kappa}}\left( {{\nu_{\overrightarrow \omega}}} \right)\) estimate of \(T\) when there is \({p_i} = 1\) are established.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B35 Function spaces arising in harmonic analysis
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