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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, 42C10, 43A80 show english descriptions Maximal functions, Littlewood-Paley theory
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Analysis on other specific Lie groups [See also 22Exx]
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]
 

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