Growth rate of the functions in Bergman type spaces |
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Authors: | Hong Rae Cho Ern Gun Kwon |
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Affiliation: | a Department of Mathematics, Pusan National University, Pusan 609-735, South Korea b Department of Mathematics Education, Andong National University, Andong 760-749, South Korea |
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Abstract: | For 0<p,α<∞, let ‖f‖p,α be the Lp-norm with respect the weighted measure . We define the weighted Bergman space Aαp(D) consisting of holomorphic functions f with ‖f‖p,α<∞. For any σ>0, let A−σ(D) be the space consisting of holomorphic functions f in D with . If D has C2 boundary, then we have the embedding Aαp(D)⊂A−(n+α)/p(D). We show that the condition of C2-smoothness of the boundary of D is necessary by giving a counter-example of a convex domain with C1,λ-smooth boundary for 0<λ<1 which does not satisfy the embedding. |
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