Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator

Abstract and Applied Analysis

Research Article

Qunfang Li¹  Huacan Li² 

[1] Department of Mathematics, Ganzhou Teachers College, Ganzhou 341000, China, gzhu.edu.cn;School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China, jxust.cn

Others  :  1320970
DOI  :  10.1155/2014/941658

 received in 2013-11-12, accepted in 2014-01-23,  发布年份 2014

【 摘 要 】

We establish the Ar(D)-weighted integral inequality for the composition of the Homotopy T and Green’s operator G on a bounded convex domain and also motivated it to the global domain by the Whitney cover. At the same time, we also obtain some (p,q)-type norm inequalities. Finally, as applications of above results, we obtain the upper bound for the Lp norms of T(G(u)) or (T(G(u)))B in terms of Lq norms of u or du.

【 授权许可】

CC BY   
Copyright © 2014 Huacan Li and Qunfang Li. 2014

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