Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications

Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications

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n this paper we introduce several iterated convolutions and establish weighted $L_p,\ p>1,-$ norm inequalities for them by using the H\"{o}lder’s inequality and the transform of integrals. Applications to wave and heat equations, Klein-Gordon equation are also considered. Especially, we wil...

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Main Authors: Nguyen Du Vi Nhan, Dinh Thanh Duc, Vu Kim Tuan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2009-01-01
Series:Armenian Journal of Mathematics
Online Access:http://test.armjmath.sci.am/index.php/ajm/article/view/44
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spelling doaj-c3d287682333448a9187dd7c6f39e7562020-11-24T23:07:16ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632009-01-0114Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their ApplicationsNguyen Du Vi Nhan0Dinh Thanh Duc1Vu Kim Tuan2Department of Mathematics, Quy Nhon University, Binh Dinh, VietnamDepartment of Mathematics, Quy Nhon University, Binh Dinh, VietnamDepartment of Mathematics, University of West Georgia, Carrollton, GA 30118, USA n this paper we introduce several iterated convolutions and establish weighted $L_p,\ p>1,-$ norm inequalities for them by using the H\"{o}lder’s inequality and the transform of integrals. Applications to wave and heat equations, Klein-Gordon equation are also considered. Especially, we will see their applications to inhomogeneous differential equations. http://test.armjmath.sci.am/index.php/ajm/article/view/44
collection DOAJ
language English
format Article
sources DOAJ
author Nguyen Du Vi Nhan
Dinh Thanh Duc
Vu Kim Tuan
spellingShingle Nguyen Du Vi Nhan
Dinh Thanh Duc
Vu Kim Tuan
Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
Armenian Journal of Mathematics
author_facet Nguyen Du Vi Nhan
Dinh Thanh Duc
Vu Kim Tuan
author_sort Nguyen Du Vi Nhan
title Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
title_short Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
title_full Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
title_fullStr Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
title_full_unstemmed Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications
title_sort weighted $l_p-$ norm inequalities for various convolution type transformations and their applications
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2009-01-01
description n this paper we introduce several iterated convolutions and establish weighted $L_p,\ p>1,-$ norm inequalities for them by using the H\"{o}lder’s inequality and the transform of integrals. Applications to wave and heat equations, Klein-Gordon equation are also considered. Especially, we will see their applications to inhomogeneous differential equations.
url http://test.armjmath.sci.am/index.php/ajm/article/view/44
work_keys_str_mv AT nguyenduvinhan weightedlpnorminequalitiesforvariousconvolutiontypetransformationsandtheirapplications
AT dinhthanhduc weightedlpnorminequalitiesforvariousconvolutiontypetransformationsandtheirapplications
AT vukimtuan weightedlpnorminequalitiesforvariousconvolutiontypetransformationsandtheirapplications
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