Parameter \(\theta\)-type Marcinkiewicz integral on nonhomogeneous weighted generalized Morrey spaces (Q2221328)

Summary: Let \((\mathcal{X},d,\mu)\) be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter \(\theta\)-type Marcinkiewicz integral \(\mathcal{M}_\theta^\rho\) is bounded on the weighted generalized Morrey space \(L^{p,\phi,\tau} (\omega)\) for \(p\in (1,\infty)\). Furthermore, the boudedness of \(\mathcal{M}_\theta^\rho\) on weak weighted generalized Morrey space \(W L^{p,\phi,\tau} (\omega)\) is also obtained.