Calderón-Zygmund operators and commutators on weak Musielak-Orlicz Hardy spaces (Q6100741)

The authors study the boundedness of Calderón-Zygmund operators and their commutators with ``BMO'' functions from weak Musielak-Orlicz Hardy spaces \(WH^\varphi({\mathbb R}^n)\) to weak Musielak-Orlicz spaces \(WL^\varphi({\mathbb R}^n)\). They formulate an appropriate proper subspace \({\mathcal{BMO}}_{\varphi,q} ({\mathbb R}^n)\) of \(\mathrm{BMO}({\mathbb R}^n)\), to get the boundedness of commutators of Calderón-Zygmund operators with \(b\in {\mathcal{BMO}}_{\varphi,q} ({\mathbb R}^n)\). \(WL^\varphi({\mathbb R}^n)\) and \(WH^\varphi({\mathbb R}^n)\) are generalizations of weighted weak \(L^p({\mathbb R}^n)\) and weighted weak Hardy spaces, respectively. So, they extend many known results.