BOUNDEDNESS OF THE BERGMAN PROJECTIONS ON Lp SPACES WITH RADIAL WEIGHTS
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چکیده
D |f(z)|dμ(z) )︀1/p < ∞ and by La(D, dμ) (or La(D) for short) the subspace of the space L(D) comprising the functions that are analytic on D. If p = 2, La(D) is a Hilbert subspace of L2(D) and it is called Bergman space. Let P denote the orthogonal projector of L2(D) on La(D) (Bergman projection). Let {δn}n=0 be defined by δn = (︀ 2π ∫︀ 1 0 r 2n+1w(r) dr )︀1/2 . Then, the sequence of functions {z/δn}n=0 is an orthonormal basis of La(D) and so the corresponding Bergman reproducing kernel is given by K(z, ξ) = ∑︀∞ n=0 z ξ n /δ2 n (z, ξ ∈ D). Let I k = [︀ k−1 n , k n ]︀ (k = 1, 2, . . . , n), Φ(λ) = ∫︀ 1 0 t 2λ+1 w(t) dt (λ ∈ (0,+∞)), G(λ) = Φ(λ+1) Φ(λ) and
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تاریخ انتشار 2009