Calderon-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-lambda f (theta) = -f '' (theta) -2 lambda cot theta f ' (theta)+lambda (2)f(theta). We prove that these operators are Calderon-Zygmund operators in the homogeneous type space ((0, pi), (sin t)2(lambda) dt). Consequently, L-p weighted, H-1 - L-1 and L-infinity - BMO inequalities are obtained.