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# A general approach to Littlewood-Paley theorems for orthogonal families

Published:1997-09-01
Printed: Sep 1997
• Kathryn E. Hare
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## Abstract

A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in $[0, 1]$, $\su$, and the usual classical trigonometric series in $[0, 2 \pi)$. The theorem is used to derive new results for $\LP$ multipliers on $\su$ and Jacobi $\LP$ multipliers.
 MSC Classifications: 42B25 - Maximal functions, Littlewood-Paley theory 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 43A80 - Analysis on other specific Lie groups [See also 22Exx]