الفهرس 
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Abstract
this thesis, we present some results in complex analysis concerning solution of [= f with estimation. First, we adapt the kernels of Ovrelid [15] to be used when is a strongly pseudo-convex domain in complex manifold X of complex Etsion n, and f is a (0,q)-form, q>l;df = 0, with values in aholomorphic tor bundle B; of rank N, over X. Let {U =} jeJ be an open covering of X for
pen BITJ. is trivial. For feL^^Dfl W,BK );df - 0;k > 1, we prove that there
a bounded linear operator maps L(0q)(Dn W,BK) into L^^^D f] W,BK), Re WccUjCll is a neighborhood of cedD,U is a neighborhood of the fcdary dD of D, and BK = B ® B is the k-times,k > 1, tensor product of B. we obtain Lp-estimates for solution of du = f on D when f e L(0 qj(D,BK), 1=0 ;k>k0;l<p<co5 which are the main results of this thesis, is thesis consists of an introduction, three chapters, and a list of references, per with arabic and english summaries. Those can be summarized as follows:
troduction: -
It includes a quick hint for the purpose of the thesis and its contents. bter 1: -
It is an introductory chapter, which contains some basic definitions. bter II: -
Bit is devoted to extend the kernels of ©vrelid [15] to be used for B -valued ^(forms on D.
(hapter 11S: -
The main results of this thesis are given in this chapter. We obtain In¬timates for solution of du = f;df = 0, on strongly pseudo-convex domain of pmplex manifold of complex dimension n, when f is a (0,q)-form, with values in a ilomorphic vector bundle B , for suitable k, I < p < co.