The following theorem is proved: let G denote a compact connected semisimple Lie group. There exists θ = θ(G) (3 ≤θ < 4) such that, if χ_1, ..., χ_N are N distinct characters of G, d_1,..., d_N their dimensions, c_1, ..., c_N complex numbers of modulus greater than or equal to one, then, for all p > θ, the L^p(G) convolutor norm of the sum Σ_{j = 1,...,N} c_j d_j χ_j is dominated by a suitable, positive power of N. Results on divergence of Fourier series on compact Lie groups are deduced.
A Cohen type inequality for compact Lie groups
GIULINI, SAVERIO;
1979-01-01
Abstract
The following theorem is proved: let G denote a compact connected semisimple Lie group. There exists θ = θ(G) (3 ≤θ < 4) such that, if χ_1, ..., χ_N are N distinct characters of G, d_1,..., d_N their dimensions, c_1, ..., c_N complex numbers of modulus greater than or equal to one, then, for all p > θ, the L^p(G) convolutor norm of the sum Σ_{j = 1,...,N} c_j d_j χ_j is dominated by a suitable, positive power of N. Results on divergence of Fourier series on compact Lie groups are deduced.
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