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math.CA2026
Characterizations of Lyapunov domains in terms of Riesz transforms and the Plemelj-Privalov theorem
Juan José Marín, José María Martell, Dorina Mitrea +1
We prove several characterizations of -domains (aka Lyapunov domains), where is a growth function satisfying natural assumptions. For example, given an Ahlfo…
math.CA2014★ 7 cited
Characterizing regularity of domains via Riesz transforms on their boundaries
D. Mitrea, M. Mitrea, J. Verdera
Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogenei…