  We construct a family of integral kernels for solving the \bar\partial
equation with C^k and Holder estimates in thin tubes around totally real
submanifolds in complex Eulidean spaces (theorems 1.1 and 3.1). Combining this
with the proof of a theorem of Serre we solve the d-equation with estimates for
holomorphic forms in such tubes (theorem 5.1). We apply these techniques and a
method of Moser to approximate C^k-diffeomorphisms between totally real
submanifolds in C^n in the C^k-topology by biholomorphic mappings in tubes, by
unimodular and symplectic biholomorphic mappings, and by holomorphic
automorphisms of C^n.
