  This paper is a survey of a new family of Banach spaces ${KS}^2$ and $SD^2$
that provide the same structure for the Henstock-Kurzweil (HK) integrable
functions as the $L^p$ spaces provide for the Lebesgue integrable functions.
These spaces also contain the wide sense Denjoy integrable functions. They were
first use to provide the foundations for the Feynman formulation of quantum
mechanics. It has recently been observed that these spaces contain the test
functions $\mathcal{D}$ as a continuous dense embedding. Thus, by the
Hahn-Banach theorem, $\mathcal{D}' \subset \mathcal{B}'$. A new family that
extend the space of functions of bounded mean oscillation $BMO[\mathbb{R}^n]$,
to include the HK-integrable functions are also introduced. We provide a few
applications. We use ${KS}^2$ to provide a simple solution to the generator
(with unbounded coefficients) problem for Markov processes. We also use $SD^2$
to provide the best possible a priori bound for the nonlinear term of the
Navier-Stokes equation.
