Function Nature Of The Space H ~ (p, A) And D ~ P Space

This dissertation deals with the properties of function in H^p,a space and D^p space on the bounded symmetric domains of Cⁿ , and the multipliers in H^p,a space, V space and between H^p,a space and D^p space.The study of analytic function spaces of one complex variable has a long time, and obtains a lot of complete results. The study of analytic function spaces in several complex variables is not only shorter than the study of analytic function space in one complex variable, but also the characterizations of function properties on analytic function spaces have been much complete. In reference [1], Kim, H. 0, Kim, S. M. and Kwon, E. G. define a new space H^p,a in one complex variable, characterize the properties of function, and give two guesses. In reference [2], Xiao, J. B. proof s one guess, and gives deeper characterizations about analytic function in H^p,a space. In this dissertation, the define about H^p,a space in reference [1] is generalized to several complex variables, the properties are characterized, and some multiplier theorem is given. In reference [3], Shi, J. H. defines the norm with Fourier coefficient of function, obtains a new space -- V space, and gives some complete characterizations of function properties. Gao, J. S. gives two multipliers on D^p space in reference [4]. The dissertation improves the results in reference [4], and gives other multiplier theorem.In the second chapter, we characterize the function in H^p,a space, and obtain the following results:Theorem2.5: If , thenTheorem2. 6: thenTheorem2. 7: If f(z ), then Theorem2. 8: If , thenwhere c is a constant not connect with f.Theorem2. 9: If then , where q = In the third chapter, we give a few function properties in D^p space.In the fourth chapter, we discuss the multipliers of D^p space H^p,a space and between H^p,a space and space, and obtain the following results:Theorem4. 9: Suppose is a multiplier of Theorem4 11: Suppose n >1. then is a multiplier of Theorem4. 16: Suppose has the propertythen is a multiplier of into Theorem4. 18: Suppose has the propertythen is a multiplier of H^p,a. into Theorem4. 22: Suppose then is a multiplier of H^p,a into...