Vaught's "*-transform method" is applied to derive a global definability theorem of M. Makkai from a classical theorem of Lusin. In a recent article [10], R. L. Vaught introduced a construction which connects the invariant descriptive set theory of "logic actions" with the model theory of the infinitary language L In this paper we will use Vaught's construction to give a short derivation of a r...

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spacesM w (l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ -function, and their multilinear commutators on vector-valued generalized weighted Morrey s...