Let G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is| Δ| 2-p, where A is the usual Weyl function. If p ≥ 2, we prove that| Δ| 2-p satisfies Muckenhoupt’s Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded
Travaglini, G. (1982). Weyl functions and A_p condition on compact Lie groups. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 33(A), 185-192 [10.1017/S1446788700018322].
Weyl functions and A_p condition on compact Lie groups
TRAVAGLINI, GIANCARLO
1982
Abstract
Let G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is| Δ| 2-p, where A is the usual Weyl function. If p ≥ 2, we prove that| Δ| 2-p satisfies Muckenhoupt’s Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded
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