“…The fine structure: Certain functions defined on a region D may constitute a reproducing kernel Hilbert space (RKHS), be denoted by H K , or H 2 (D), and called the Hardy space of the context, where K : D × D → C is the reproducing kernel, K q (p) = K(p, q), p, q ∈ D. In such case the boundary values, or the non-tangential boundary limits, as often occur in harmonic analysis, span a dense class of H = L 2 (∂D) (as a new notation), or sometimes just dense in a proper subspace of H. In the case the boundary value mapping induces an isometry, or a bounded linear operator, between H 2 (D) and H 2 (∂D). The related theory and examples are contained in [27], [16], [20], as well as in [32]. The relevant literature address various types of RKHSs, or Hardy spaces in such setting, including, for instance, the H 2 space of complex holomorphic functions in the unit disc D 1 , and the h 2 space of harmonic functions in the upper-half Euclidean space, precisely,…”