Ngày tải lên :
21/06/2014, 06:20
... occurrence Littlewood-Paley g- Function on K ∗ Let k ∈ N, then we define the following G- function and g -function gk f ∞ x, t ∗ gk f ∞ x, t − α K s −2 s k P s f x, t s y, r k s 2k 1 ds, s ∂s P T α y,r ... k > α /2, we know K k y, r dmα y, r < ∞ 2.12 By Proposition 1.3, K ∗ gk f x, t ψ x, t dmα x, t ∞ K K ≤C K ∞ K s− α s− α s−2 k y, r ∂s P s f y, r g1 f ≤ C g1 f 1 ∂s P s T s−2 α K α y,r T x,t ... 2.1 a For k ∈ N and f ∈ L2 K , there exists Ck > such that gk f α,2 Ck f α,2 2.2 b For < p < ∞ and f ∈ Lp K , there exist positive constants C1 and C2 , such that C1 f c If k > α α,p ≤ gk f α,p...