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1. CJM 2007 (vol 59 pp. 1223)

Buraczewski, Dariusz; Martinez, Teresa; Torrea, José L.
 CalderÃ³n--Zygmund Operators Associated to Ultraspherical Expansions We define the higher order Riesz transforms and the Littlewood--Paley $g$-function associated to the differential operator $L_\l f(\theta)=-f''(\theta)-2\l\cot\theta f'(\theta)+\l^2f(\theta)$. We prove that these operators are Calder\'{o}n--Zygmund operators in the homogeneous type space $((0,\pi),(\sin t)^{2\l}\,dt)$. Consequently, $L^p$ weighted, $H^1-L^1$ and $L^\infty-BMO$ inequalities are obtained. Keywords:ultraspherical polynomials, CalderÃ³n--Zygmund operatorsCategories:42C05, 42C15frcs
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