Uniform Estimates Of Solutions Of (?)-Equations On Local Q-Concave Wedges In Stein Manifolds

A local q-concave wedge is an important class of domains, it has been vastly used to discuss CR manifolds, tangential Cauchy-Riemann equations, holomorphic extensions of CR-functions and (?)-cohomology. For q=n-1, a local q-concave wedge is simply the intersection of a piecewise smooth strictly pseu-doconcave domain with a convex domain, therefore a local q-concave wedge represents a large class of domains. C. Laurent-Thiebaut & J. Leiterer^[13] obtained the Cauchy-Riemann equation for (n,r) differential forms on Q-concave wedges of Cⁿ and uniform estimate for the (?)-equation. Further, by means of the Hermitian metric and Chern connection, Tongde Zhong^[16-17] obtained the Koppelman-Leray-Norguet formula, homotopy formula and the solutions of (?)-equation for (r,s) differential forms on a local q-concave wedge in Stein manifolds. On the base of [16,17], by means of the ideas of J. P. Demailly & C. Laurent-Thiebaut^[8] and the trick of Rang-Siu^[14], the author obtains uniform mestimates of the solutions of (?)-equation for (r,s) differential forms on local q-concave wedges on Stein manifolds.The dissertation includes three chaptes:In the first chapter, the author introduces some definitions, the basic lemma on local q-concave wedges in Stein manifolds, including local q-concave wedge, the subminifoldГ_K, a Leray map for local q-concave wedge and so on.In the second chapter, the author introduces the operator M and H, homotopy formula for local q-concave wedges and the solutions of (?)-equations, including the singularity of kernel H.In the third chapter, the author obtains the uniform estimate of solutions of (?)- equation and the main result of this paper.