A remark on averaging operators on homogeneous spaces

摘要

To any sequence $ g_1,..., g_d, g{-1 atop 1},..., g{-1 atop d} $ in a group G one can associate an averaging operator acting on functions on a homogeneous space of G. For a connected compact Lie group G we obtain a lower bound for the L 2-norm of this operator in the orthocomplement to the constants.