On. Stein Manifold Plemelj Formula Of The Cauchy Type Integral On A Bounded Domain (?) - Equation

Plemelj Formula of Cauchy Type Intergrals on Stein Manifolds and &-Equation on Bounded DomainsChen LüpingAbstract:In the first chapter of the present paper,the author assume D bea bounded domain with piecewise C1 smooth boundary in Stein manifold,^z bea.int;ergra.] of Ca.tichy t;ype with Bochner-Martinelli kernel and Holder continuitydensity function, then the author defines a solid angle coefficient a(t) at thepoint t^aD,proves thaot existing interior and outer limit values and4Y (z) ,and the author establishes a more general Plemelj formula. In the secondchapter of the present paper ,the author overcomes the difficulty that there doesn't exist global solutions of 8- equation on a general bounded domain,o.btains the following result:Let D be a bounded domain in, such that c9g = O,then exists a local differential solution of equation t^u = g in D which is,and u has an inner closed uniform estimate in D,i.e. where cl(12) is Bochner-Martinelli kernel and ^H is a local differential kernel,C is a cdnstant.