Abstract |
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By using the Cauchy–Fantappiè
machinery, the nonhomogeneous Cauchy-Riemann equation on convex
domain D for (0,q) form f with
∂f =
0, ∂u =
f, has a solution which is a linear
combination of integrals on bD of
the following differential forms
j = 1,⋯,n
− q − 3, where
A = ⟨∂ζr(ζ),ζ
− z⟩,
β = |z − ζ|2 and
r is the defining function of
D. In the case of finite
strict type, Bruna et al. estimated ⟨∂r(ζ),ζ
−z⟩ by the
pseudometric constructed by McNeal. We can estimate the above
differential forms and their derivatives. Then, by using a
method of estimating integrals essentially due to McNeal and
Stein, we prove the following almost sharp Hölder estimate
for arbitary κ
> 0. The constant only depends on κ,D and q.
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Authors
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Berkeley, California.