The following theorem is proved: Let G denote a compact connected semisimple Lie group. There exists ø — ø(G) (3 < ø < 4) such that, if X1> • • •, XN are N distinct characters of G, d1.dN their dimensions, C1.cN complex numbers of modulus greater than or equal to one, then, for all p > ø, III∑Nj-1cjdjxjIIIp, > constp, Na p where III’ IIIp, denotes the LP(G) convolutor norm and constp, and ap = ap(G) are positive constants. Results on divergence of Fourier series on compact Lie groups are deduced

Giulini, S., Soardi, P., Travaglini, G. (1979). A Cohen type inequality for compact Lie groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 77(3), 359-364 [10.1090/S0002-9939-1979-0545596-3].

A Cohen type inequality for compact Lie groups

SOARDI, PAOLO MAURIZIO;TRAVAGLINI, GIANCARLO
1979

Abstract

The following theorem is proved: Let G denote a compact connected semisimple Lie group. There exists ø — ø(G) (3 < ø < 4) such that, if X1> • • •, XN are N distinct characters of G, d1.dN their dimensions, C1.cN complex numbers of modulus greater than or equal to one, then, for all p > ø, III∑Nj-1cjdjxjIIIp, > constp, Na p where III’ IIIp, denotes the LP(G) convolutor norm and constp, and ap = ap(G) are positive constants. Results on divergence of Fourier series on compact Lie groups are deduced
Articolo in rivista - Articolo scientifico
Compact Lie groups, Convolutors, Dirichlet kernels
English
1979
77
3
359
364
none
Giulini, S., Soardi, P., Travaglini, G. (1979). A Cohen type inequality for compact Lie groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 77(3), 359-364 [10.1090/S0002-9939-1979-0545596-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18286
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