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A general approach to Littlewood-Paley theorems for orthogonal families |
Canad. Math. Bull. 40(1997), 296-308
Published:1997-09-01
Printed: Sep 1997
Printed: Sep 1997
- Kathryn E. Hare
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] |