Dự toán thiết bị đầu cuối trọng cho số ít các nhà khai thác multilinear thể tách rời với hạt nhân Calder'n Zygmund biến trên một số Hardy và Hardy loại Herz không gian o thu được. | Vietnam Journal of Mathematics 34 Viet n a m J o u r n a I of MATHEMATICS VAST 2006 Weighted Estimates of Multilinear Singular Integral Operators with Variable Calderon-Zygmund Kernel for the Extreme Cases Liu Lanzhe College of Math. and Compt. Changsha Univ. of Sci. and Tech. Changsha 410077 China Abstract. . 1. Introduction 1 . . 1 Supported by the NNSF Grant 10271071 . Liu Lanzhe 2. Notations and Theorems A. . . x e . tt L tt . . . _ Definition 1. . be two non-negative weight functions on . The homogeneous weighted Herz space is defined by K. . . . . . where tt . . . . 1 . 2 L 2 tt The nonhomogeneous weighted Herz space is defined by . . . 1. 2 where tt _ K . L . 2 The homogeneous weighted Herz type Hardy space is defined by . . where . . . . 1 . 2 . . 1. 2 The nonhomogeneous weighted Herz type Hardy space is defined by Weighted Estimates of Multilinear Singular Integral Operators . . . . . . where A 1- 2-. 1- 2- and A AA is the grand maximal function of A . . Definition 2. A . A A . A A . A function A AA A on A is called a .A-atom or a .A-atom of restrict type if 2 2 2 L 2 1 Lemma 1. .Let A .AA . A A . temperate distri- bution A belongs to A K .AA . A A . A A or .AA . A A . A a if and only if there exist A .A-atoms or central. .A A .A-atoms of restrict type A. supported on . A and constants A. . . A A A such that A j A A. A. or A 00 A. A. in the A A sense and A 1 2-A or A A A 1 2 A A AA Definition 3. Let. A A . is said to be a Calderon-Zygmund kernel if . AA a. AAA is homogeneous of degree zero . .for all multi-indices. with. 2 where. .is the unit sphere of A . Definition 4. Let. A A AA . . is said to be a variable Calderon-Zygmund kernel if .is kernel for . A A A .I. I. . ụ. A A A . r . Let be a positive integer and A be a function on A . Set A . . D . . .
