| This thesis mainly discuss the multiplier theory of Complex Analysis. Tt is divided into four chapters: the first chapter, we give the purpose and meaning of studying multipli-er, the research status of multiplier at home and abroad, the main content and structure in this paper. The second chapter, this paper studies multiplier emphasis on the unit disk and obtains a sufficient condition of multiplier from Hp,α space to weighted Bergman space Ap,q,β;through massive researches, this paper also gets a sufficient condition of multiplier from Hp,α space to complex sequence space lq on bounded symmetric domain Ω. The purpose of chapter two is to obtain complementary multiplier nature of Hp,α, in order to make function property complete in this space. the third chapter, we mainly studied mul-tiplier theory between Ap and Hq on bounded symmetric domains, we also give multiplier property of space Ap,q,α to sequence ls. This chapter mainly promote part conclusion in reference [7]; In fourth chapter,we make a summarize of the main conclusions of this thesis, and give the difficulties of multiplier I meet when I study multiplier theory and the multiplier direction we should work hard at.This thesis mainly promote the related multiplier results in single Complex Variable function. The main four conclusions in this thesis:Theorem 2.1 Suppose 0 < p < 1 ≤ q <∞,0< α ≤ 1,0<β<∞, if (?)satisfies Mq(r,h[α/p]) = O((1 - r)-α-(β+1)/p), then {λn} ∈ (Hp,α,Ap,q,β).Theorem 2.2 Suppose 0<p<q≤1,0<α<1,if {λk} satisfies(?)then {λk} is multiplier from Hp,α(Ω) to lq.Theorem 3.1 Suppose p = 1,2 (?),then {λk}∈[(H1(Ω),Aq(Ω)).Theorem 3.3 In bounded symmetrical domain C~n, suppose 0 < p≤ s,0 < q≤ 1,-1<α <∞ ,if sequence of complex numbers{λk} satisfies (?), then{λk}∈(Ap,q,α(Ω),ls), in turn, for Ω = Bn,the condition (*) is also a necessary condition. |
