CALDERÓN-ZYGMUND OPERATORS ASSOCIATED TO ULTRASPHERICAL EXPANSIONS

Abstract. We define the higher order Riesz transforms and the Littlewood-Paley g-function associated to the differential operator Lλf(θ) = −f ′′(θ) − 2λ cot θf ′(θ)+λ2f(θ). We prove that these operators are Calderón-Zygmund operators in the homogeneous type space (0, pi), (sin t)2λ dt. Consequently