Abstract
UDC 517.5 The relationship between smoothness properties of the boundary of a domain Ω and the boundedness of the Beurling transform in the corresponding Lipschitz classes Lip(ω) for the case of a Diniregular module of continuity ω is studied. The result is sharp. Our motivation arises from the work of Mateu, Orobitg, and Verdera. Bibliography: 8 titles.
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