Some Properties Of Holomorphic And Pluriharmonic Functions Of C~n

Multiplier theory having a long history. In the language of multiplier the conclusion of Hardy-Littlewood interpret three classic problems of complex analysis. Based on the research of single-dimensional multipliers, many authors then do some research in multidimensional multipliers.Watanable and Stojan considerer the problems of determining the space A p to which f belongs if f ~′belongs to A~ q.In other words ,the language of multiplier theory says to find q ,such thanIn the second section of this paper, we consider the same problems in bounded symmetric domains and get the result in the following: If 0 < p < n+ 1, ( )f [1]∈A~pΩ.ThenWe generalize the above result and get results in the following: Let 0≤α<∞.If f′∈Aψp,αfor some p , 0 < p< 2,then f∈Aψq ,γ,where q = 2 p ( 2? p),γ=α(1 + q /2)andψq is quasi-normal. If f′∈A2,Then f∈BMOA.But there exists a function f 0 is analytic in z < 1, such thatLet 0≤α<∞andψqbe quasi-normal.If 0 < p<∞, 0 <β< 2 / p,and f [β]∈Aψp,α. Then f∈Aψq,γ,where q = 2 p / ( 2?βp),γ=α(1 +βq /2).If 0 < p≤2, f [ 2/ p ]∈Ap,then f∈BMOA.But there exists a function f 0, such thaWe study the multipliers related A ~p(Ω) in the third part of this paper and get the results in the following: If 1≤p<∞.Then {λn }∈( A ~p,β)if and only if where1 / p + 1 / q= 1, If1≤p<∞,1≤q < 2 ,Then...