On Carleson-Type Embeddings for Bergman Spaces of Harmonic Functions
Tóm tắt
Given a measure μ on a bounded domain Ω ⊂ ℝn with C1 boundary, we investigate the following problem: when is a weighted harmonic Bergman space
$$A_\alpha^p(\Omega)$$
continuously embedded in weighted space Lp(Ω) = Lp(μ, Ω)? We give a sufficient Carleson type condition for all α > −1 and 0 < p < ∞ which is also necessary for
$$p > 1 + \frac{{\alpha + 2}}{{n - 2}}$$
.
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