Dual spaces of multiparameter local Hardy spaces (Q2064451)

Summary: In this paper, we study the duality theory of the multiparameter local Hardy spaces \(h^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\), and we prove that \((h^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2}))^\ast=\mathrm{cmo}^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\), where \(\mathrm{cmo}^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\) are defined by discrete Carleson measure. Moreover, we discuss the relationship among \(\mathrm{cmo}^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\), \(\mathrm{Lip}^p( \mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\), and rectangle \(\mathrm{cmo}_{\mathrm{rect}}^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\).