The Dual of the Space of Regulated Functions in Several Variables
We consider a class of regulated functions of several variables, namely, the class of functions φ defined in an open set UR^n such that at each x_0U the \[φ_x_0 ( w) =_ε →0^+ φ(fx_0+εw) \] exists uniformly on wS, the unit sphere of R^n, and such that φ_x_0 is a continuous function of w at each x_0U. We identify the elements of the dual spaces of several Banach space of such regulated functions in several variables as signed measures with absolutely convergent sums of “ thick” delta functions concentrated at a countable set. , number=2, journal=Sarajevo Journal of Mathematics, author=Yang, Yunyun and Estrada, Ricardo, year=2024, month=Jun., pages=197–216