Boundedness of Commutators for Multilinear Marcinkiewicz Integrals with Generalized Campanato Functions on Generalized Morrey Spaces (Journal of Mathematical Study, 2023)
This paper is devoted to exploring the mapping properties for the commutator $μ_{Ω,\vec{b}}$ generated by multilinear Marcinkiewicz integral operators $μ_Ω$ with a locallyintegrable function $\vec{b}= (b_1,···,b_m)$ on the generalized Morrey spaces. $μ_{Ω,\vec{b}}$ is boundedfrom $L^{(p_1,φ_1)} (\mathbb{R}^n)×···×L^{(p_m,φ_m)} (\mathbb{R}^n)$ to $L ^{(q,φ)} (\mathbb{R}^n),$ where $L^{(p_i,φ_i)} (\mathbb{R}^n),$ $L^{(q,φ)} (\mathbb{R}^n)$ aregeneralized Morrey spaces with certain variable growth condition, that $b_j(j=1,···,m)$ is a function in generalized Campanato spaces, which contain the BMO$(\mathbb{R}^n)$ and theLipschitz spaces ${\rm Lip}_α(\mathbb{R}^n) (0