Abstract
Let μ be the normalized Lebesgue measure on S n −1. For x = (x 1,…,x n ) with ||x||2 < 1 we denote by μx the probability measure on S n −1 given by \( \frac{{1 - {{\left\| x \right\|}^2}}} {{{{\left\| {y - x} \right\|}^n}}}d\mu \left( y \right) \). We recall that if f is an integrable function on S n -1 then u(x) = \( u(x) = {\int_{{S^{n - 1}}} {f(y)d\mu }^x}(y) \) is a harmonic function whose radial limits are equal μ-almost everywhere to f.
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Schechtman, G., Schmuckenschläger, M. (1995). A Concentration Inequality for Harmonic Measures on the Sphere. In: Lindenstrauss, J., Milman, V. (eds) Geometric Aspects of Functional Analysis. Operator Theory Advances and Applications, vol 77. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9090-8_22
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DOI: https://doi.org/10.1007/978-3-0348-9090-8_22
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