Elementary characterizations of generalized weighted Morrey-Campanato spaces  

作　　者：YANG Da-chun YANG Si-bei 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第2期162-176,共15页高校应用数学学报（英文版）（B辑）

基　　金：supported by the National Natural Science Foundation of China(10871025)

摘　　要：Let α∈（0,∞ ）, p, q ∈[1, ∞）, s be a nonnegative integer, and ω∈ A1（Rn） （tne class of Muckenhoupt＇s weights）. In this paper, we introduce the generalized weighted Morrey- Campanato space L（α, p, q, s, ω; Rn） and obtain its equivalence on different p∈ [1, β） and 1 integers s ≥[nα] （the integer part of nα）, whereβ = （1/q - α）-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A（α, q, w; Rn） and prove that L（a, p, q, s, w; Rn）С ∧（α, q, w; Rn） when α ∈ （0, ∞）, s ≥[nα], and p∈ [1,β）.Let α∈（0,∞ ）, p, q ∈[1, ∞）, s be a nonnegative integer, and ω∈ A1（Rn） （tne class of Muckenhoupt＇s weights）. In this paper, we introduce the generalized weighted Morrey- Campanato space L（α, p, q, s, ω; Rn） and obtain its equivalence on different p∈ [1, β） and 1 integers s ≥[nα] （the integer part of nα）, whereβ = （1/q - α）-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A（α, q, w; Rn） and prove that L（a, p, q, s, w; Rn）С ∧（α, q, w; Rn） when α ∈ （0, ∞）, s ≥[nα], and p∈ [1,β）.

关 键 词：Morrey-Campanato space Lipschitz space weight. 

分 类 号：O175.2[理学—数学] O159[理学—基础数学]