摘要
Let L be the infinitesimal generator of an analytic semigroup on L2 （R^n） with suitable upper bounds on its heat kernels. Assume that L has a bounded holomorphie functional calculus on L^2（R^n）. In this paper, we define the Littlewood-Paley g function associated with L on R^n × R^n, denoted by GL（f）（x1,x2）, and define the area function, denoted by SL（f）（x1,x2）. Using a vector-valued version of Calderon-Zygmund decomposition, we prove that ｜｜SL（f）｜｜p≈｜｜GL（f）｜｜p ≈ ｜｜f｜｜p for 1 〈 p 〈 ∞.
Let L be the infinitesimal generator of an analytic semigroup on L2 （R^n） with suitable upper bounds on its heat kernels. Assume that L has a bounded holomorphie functional calculus on L^2（R^n）. In this paper, we define the Littlewood-Paley g function associated with L on R^n × R^n, denoted by GL（f）（x1,x2）, and define the area function, denoted by SL（f）（x1,x2）. Using a vector-valued version of Calderon-Zygmund decomposition, we prove that ｜｜SL（f）｜｜p≈｜｜GL（f）｜｜p ≈ ｜｜f｜｜p for 1 〈 p 〈 ∞.
基金
Supported by NNSF of China and the Foundation of Advanced Research Center, Zhongshan University.
