Atomic Decomposition Of μ-Bergman Space In C~n

In this article, we studied the atomic decomposition of the μ-Bergman space on unit ball in Cn and the approximation of the function in μ-Bergman space. At the same time, we discussed the pointwise estimateatoms of the μ-Bergman function on the unit ball as well as the compactness conditions of the multiplier operator in the μ-Bergman space.It consists of three chapters.In the first chapter, We has carried on the comprehensive summary of the research background as well as the conclusion about the two two plates of this article.In the second chapter, we discussed the atomic decomposition of μ-Bergman space on unit ball in Cn. First of all, a practical estimate inequality are given, namely theorem 2.3.1. The second is presented the specific atomic decomposi-tion form of functions in μ-Bergman space, namely theorem 2.3.2. Some math-ematical workers have been discussed the problem on the weighted Bergman space Aαp. In this article, we extend the weight (1-|z|2)α to the normal weightIn the third chapter, We mainly discussed three questions of the μ-Bergman space on unit ball:One is the problem of function approximation, the function-s in μ-Bergman space can be close to the polynomial in accordance with the norm of the space, namely theorem 3.2.1. The second is the pointwise estimate of functions when the fixed point tends to boundary of the unit ball, namely theorem 3.2.2, that estimate is more accurate than the existing inequality es-timation inside the unit ball. The third is the compactness conditions of the multiplier operator, it is presented that the sufficient and necessary condition of multiplier operator in μ-Bergman space to be the compact operator is zero multiplier, namely theorem 3.2.3.