The Homogeneous Approximation Property in the Bergman Space
نویسندگان
چکیده
It is shown that sets of sampling for the Bergman space A2 have the “homogeneous approximation property” (HAP) and that sets with this property are sampling for A 2+E. In addition, previous results concerning the boundary behaviour of sampling sets are improved. ForO<p<oo, the Bergman space AP is the set of functions f analytic in the unit disk D = (2 : 1.~1 < 1) with where dA denotes Lebesgue area measure. If p 2 1, AP is a Banach space with norm (1 . Ilp. If 0 < p < 1, it is a complete metric space, where the metric is given by d(.f,g) = Ilf 911;. A2 is a Hilbert space with inner product
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