Resumen de Duality of central Herz–Morrey–Musielak–Orlicz spaces of variable exponents

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura

• Our aim in this paper is to establish duality of central Herz-Morrey-Musielak-Orlicz spaces \mathcal {H}^{\Phi ,q(\cdot ),\omega }(\mathbf{R}^N_0) of variable exponents, the space \underline{\mathcal {H}}^{\Phi ,q(\cdot ),\omega }(\mathbf{R}^N_0) and its complementary space \overline{\mathcal {H}}^{\Phi ,q(\cdot ),\omega }(\mathbf{R}^N_0) by studying the associate spaces of central Herz-Morrey-Musielak-Orlicz spaces \mathcal {H}^{\Phi ,q_1,q_2,\omega }(\mathbf{R}^N_0), the space \underline{\mathcal {H}}^{\Phi ,q_1,q_2,\omega }(\mathbf{R}^N_0) and its complementary space \overline{\mathcal {H}}^{\Phi ,q_1,q_2,\omega }(\mathbf{R}^N_0).