Mục đích của bài viết này là để nghiên cứu tính chất boundedness multilinear Littlewood-Paley các nhà khai thác cho các trường hợp cực kỳ. | Vietnam Journal of Mathematics 33 2 2005 123-134 V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 Boundedness of Multilinear Littlewood-Paley Operators for the Extreme Cases Liu Lanzhe College of Mathematics Changsha University of Science and Technology Changsha 410077 China Received July 7 2003 Revised December 4 2004 Abstract. The purpose of this paper is to study the boundedness properties of multilinear Littlewood-Paley operators for the extreme cases. 1. Introduction and Results . . R- . . . . r . . r . This work was supported by the NNSF Grant 10271071 . 124 Liu Lanzhe R R. . . . R 1 R t. . R .R .B - . - . B Boundedness of Multilinear Littlewood-Paley Operators for the Extreme Cases 125 Theorem 1. D .R for. Then is bounded from . R . to . R . Theorem 2. .R . for. Then is bounded from . R . to .R . Theorem 3. .R for. Then is bounded from . R . to weak - R . Theorem 4. .R . for. If for any -atom supported on certain cube and. there is . . .-------------- . . . . then is bounded from R to . R . If for any cube and. there is . . N- then is bounded from .R . to .R . 2. Proofs of Theorems Lemma . be a function on R and . . R . for. and some . Then . . 1 q - .- . . . where .is the ball centered at. and having radius . Lemma 2. Let. .and . .R . for. . . Then is bounded from . R . to . that .
