Lusin area integrals related to Jacobi expansions

Abstract

We investigate mixed Lusin area integrals associated with Jacobi trigonometric polynomial expansions. We prove that these operators can be viewed as vector-valued Calderón-Zygmund operators in the sense of the associated space of homogeneous type. Consequently, their various mapping properties, in particular on weighted $L^p$ spaces, follow from the general theory.

16 pages

References in corpus (3)

• Riesz-Jacobi transforms as principal value integrals
• An L^1-estimate for certain spectral multipliers associated with the Ornstein--Uhlenbeck operator
• Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces