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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 ‖u‖ C 1 m −κ 0,q−1 (D) ≤ C‖f‖L∞0,q(D), 1 ≤ q ≤ n − 1

Hölder regularity for ∂ on the convex domains of finite strict type