Calderón–Zygmund Operators and Commutators on Weak Musielak–Orlicz Hardy Spaces

In this paper, we study the boundedness of δ-Calderón–Zygmund operators and their commutators from weak Musielak–Orlicz Hardy spaces to weak Musielak–Orlicz spaces. To obtain the boundedness of a commutator of δ-Calderón–Zygmund operator generated by a locally integrable function, we introduce a non-trivial subspace of BMO(R^n) and prove that the commutator of a δ-Calderón–Zygmund operator is bounded from a weak Musielak–Orlicz Hardy space to a weak Musielak–Orlicz space if the locally integrable function belongs to such a subspace of BMO (R^n).