Atomic decomposition in regulated domains


Abstract


We obtain atomic decomposition formulas for weighted Bergman spaces A_{𝛼}<sup>p</sup>(ω), 𝛼 > -1, 1 < p < ∈fty, where ω ∈ Bbb C belongs to the class of regulated domains. We are able to construct atomic decomposition directly on a give regulated domain ω by using its geometric properties.

DOI Code: 10.1285/i15900932v24n1p65

Keywords: Atomic decomposition; Bergman space; Regulated domains; Reproducing kernel

Classification: 46E15; 46B03; 47B37; 30H05; 30C20

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