A Concentration Inequality for Harmonic Measures on the Sphere

  • Gideon Schechtman
  • Michael Schmuckenschläger
Part of the Operator Theory Advances and Applications book series (OT, volume 77)


Let μ be the normalized Lebesgue measure on S n −1. For x = (x 1,…,x n ) with ||x||2 < 1 we denote by μ x 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.


Brownian Motion Lipschitz Function Lipschitz Constant Harmonic Measure Absolute Constant 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Gideon Schechtman
    • 1
  • Michael Schmuckenschläger
    • 1
    • 2
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.J. Kepler UniversitätLinzAustria

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