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# The behaviour of Legendre and ultraspherical polynomials in $L_p$-spaces

Published:1998-12-01
Printed: Dec 1998
• N. J. Kalton
• L. Tzafriri
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## Abstract

We consider the analogue of the $\Lambda(p)-$problem for subsets of the Legendre polynomials or more general ultraspherical polynomials. We obtain the best possible'' result that if \$2
 MSC Classifications: 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 33C45 - Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] 46B07 - Local theory of Banach spaces

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