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

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

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...

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Main Authors: Huacan Li, Qunfang Li
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/941658
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spelling doaj-260469c00fe94cbe9d215752ae3b31a12020-11-25T01:02:10ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/941658941658Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s OperatorHuacan Li0Qunfang Li1School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaDepartment of Mathematics, Ganzhou Teachers College, Ganzhou 341000, ChinaWe 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.http://dx.doi.org/10.1155/2014/941658
collection DOAJ
language English
format Article
sources DOAJ
author Huacan Li
Qunfang Li
spellingShingle Huacan Li
Qunfang Li
Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
Abstract and Applied Analysis
author_facet Huacan Li
Qunfang Li
author_sort Huacan Li
title Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
title_short Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
title_full Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
title_fullStr Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
title_full_unstemmed Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator
title_sort some weighted norm estimates for the composition of the homotopy and green’s operator
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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.
url http://dx.doi.org/10.1155/2014/941658
work_keys_str_mv AT huacanli someweightednormestimatesforthecompositionofthehomotopyandgreensoperator
AT qunfangli someweightednormestimatesforthecompositionofthehomotopyandgreensoperator
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