| Abstract: | 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 holomorphic functional calculus on L2 (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 Calderón-Zygmund decomposition, we prove that ∥SL(f)∥p ≈ ∥GL(f)∥p ≈ ∥f∥p for 1 < p < ∞.
Supported by NNSF of China and the Foundation of Advanced Research Center, Zhongshan University. |
