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Assume that Mobius transformations f and g generate a discrete group. We obtain the following generalizations of J0rgensen's inequalities. If tr(fgf I g-1) i 1, then I tr2(f) 21 + I tr(fgfIg-I) 1 > 1… (More)
Let g(x) be a p-quasisymmetric function. Then the dilatation K(z) of Beurling-Ahlfors extension with r = 1 satisfies the inequalitites K < 2p 7(p 1)/6(p + 1) and K < 2p 2 + O(l/p) for sufficiently… (More)