Geodesic
Calderón–Zygmund Operators Associated to Ultraspherical Expansions
Canadian journal of mathematics, Tome 59 (2007) no. 6, pp. 1223-1244

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We define the higher order Riesz transforms and the Littlewood-Paley $g$ -function associated to the differential operator ${{L}_{\lambda }}f(\theta )\,=\,-{f}''(\theta )-2\lambda \cot \theta {f}'(\theta )+{{\lambda }^{2}}f(\theta )$ . We prove that these operators are Calderón–Zygmund operators in the homogeneous type space $((0,\,\pi ),\,{{(\sin t)}^{2\lambda }}dt)$ . Consequently, ${{L}^{p}}$ weighted, ${{H}^{1}}\,-\,{{L}^{1}}$ and ${{L}^{\infty }}\,-\,BMO$ inequalities are obtained.
DOI : 10.4153/CJM-2007-052-2
Mots-clés : 42C05, 42C15, ultraspherical polynomials, Calderón–Zygmund operators 
Buraczewski, Dariusz; Martinez, Teresa; Torrea, José L. Calderón–Zygmund Operators Associated to Ultraspherical Expansions. Canadian journal of mathematics, Tome 59 (2007) no. 6, pp. 1223-1244. doi: 10.4153/CJM-2007-052-2
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