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# An Application of Ricci-Stein Theorem to Estimates of the C-R Equations

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An Application of Ricci-Stein Theorem to Estimates of the C-R Equations book

# An Application of Ricci-Stein Theorem to Estimates of the C-R Equations

DOI link for An Application of Ricci-Stein Theorem to Estimates of the C-R Equations

An Application of Ricci-Stein Theorem to Estimates of the C-R Equations book

## ABSTRACT

Let n be a bounded, open subset in Cn+l with smooth boundary studying

mainly centered around the question of the integral representation of the

strongly pesudoconvex domains, the solutions are quite complete , see Krantz

Do we have corresponding estimates in weakly pseudo-convex domains? In

t 2 , the results of Chang-Nagel-Stein [CNS], Christ [Ch] , Kohn-Fefferman [KF],

Nagel-Rosay-Stein-Wainger [NRSW] shows the solution of the a-equation which

maps L"' to A112m and S~ to where 2m is the "type" of the domain and are the non-isotropic Sobolev spaces. In this paper, we compute the

integral kernel for the Henkin solution H on domains

52 Der-Chen Chang

Thus the problem reduces to getting the sharp estimates for these kernels

R(f) (x) <K(x,•l,flaH >, where f e C~(8Hm). m,x

8H is a smooth submanifold passing through x, which is defined by m,x

T(f)(w' ,s) = J e2 im!m[ lz' 12m-2(z'•w')] K (z' w' t-s)f (z' t)dz'. p+~ • • p •

w' variables which allows us to apply Ricci-Stein's theorem [RS] to get the

An Application of Ricci-Stein Theorem 53

domains (even more general domains) which allows us to follow the Kerzman-

Szego kerne 1.