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THE FUNDAMENTAL THEOREM OF CALCULUS
In the present paper we give the Fundamental Theorem of Calculus RR for the variational or Henstock vector integrals KR α df and KR dα f of multidimensional Banach space-valued functions. Introduction In [1, Proposition 3.2], Bongiorno and Di Piazza gave a characterization of the functions which are Kurzweil-Henstock vector integrals of the form h(t)=K [...]
Isomorphism Theorems for Pseudo-Runge Pairs Basic Estimates
§ 1. Basic Estimates Let X be an n-dimensional complex manifold with a complete hermitian metric ds2, and let £ be a holomorphic vector bundle over X with a hermitian metric h along the fibers. Definition 1.1. We say that the basic estimate holds at bi-degree (p, q) if there exist a compact subset KaX [...]
Theorem 1.5 Under the above notations
(20) -’ Here Tf denote the adjoints of T{. T) is a multiplication of a Hom(£, £)-valued (1, l)-form. We set (21) -Dl = e(0h 0heCl-*(X, Horn (£,£)). 0h is called the curvature form of E with respect to h. Then (20) becomes (22) |- ( || 9Ef || 2 + 1| 8f || 2) [...]
