First, we extend the criteria for smooth points of from [22] to the whole class of Musielak-Orlicz spaces. Next, we present criteria for very smooth and strongly smooth points of .
Relations are established between several notions of solidity in vector-valued sequence spaces, and a generalized Köthe-Toeplitz dual space is introduced in the setting of a Banach algebra.
Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.