Calderón–Zygmund Operators Associated to Ultraspherical Expansions

Abstract

Abstract We define the higher order Riesz transforms and the Littlewood–Paley g -function associated to the differential operator L λ f (θ) = – f ′′(θ)–2λ cot θ f ′(θ) + λ 2 f (θ). We prove that these operators are Calderón–Zygmund operators in the homogeneous type space ((0, π), (sin t ) 2λ dt ). Consequently, L p weighted, H 1 – L 1 and L ∞ – BMO inequalities are obtained.

Locations

• Canadian Journal of Mathematics - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF