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The necessary and sufficient conditions for the existence of a kind of Hilbert-type multiple integral inequality with the non-homogeneous kernel and its applications
- Source :
- Journal of Inequalities and Applications, Vol 2017, Iss 1, Pp 1-12 (2017)
- Publication Year :
- 2017
- Publisher :
- SpringerOpen, 2017.
-
Abstract
- For ${x}= ( {x}_{1},\ldots, {x}_{{n}} )$ , ${u} ( {x} ) = ( \sum_{{i}=1}^{{n}} {a}_{{i}} {x}_{{i}}^{\rho} )^{1/\rho}$ , ${v} ( {y} ) = ( \sum_{{i}=1}^{{n}} {b}_{{i}} {y}_{{i}}^{\rho} )^{1/\rho}$ , by using the methods and techniques of real analysis, the sufficient and necessary conditions for the existence of the Hilbert-type multiple integral inequality with the kernel ${K} ( {u} ( {x} ),{v} ( {y} ) ) ={G} ( {u}^{\lambda_{1}} ( {x} ) {v}^{\lambda_{2}} (y) )$ and the best possible constant factor are discussed. Furthermore, its application in the operator theory is considered.
- Subjects :
- Applied Mathematics
Multiple integral
lcsh:Mathematics
010102 general mathematics
Type (model theory)
Operator theory
Homogeneous kernel
lcsh:QA1-939
01 natural sciences
010101 applied mathematics
Constant factor
Combinatorics
Kernel (algebra)
bounded operator
operator norm
best possible constant factor
Non homogeneous
sufficient and necessary conditions
Discrete Mathematics and Combinatorics
Hilbert-type inequality
0101 mathematics
non-homogeneous kernel
Analysis
Mathematics
Subjects
Details
- Language :
- English
- Volume :
- 2017
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Inequalities and Applications
- Accession number :
- edsair.doi.dedup.....fe723a34f8480fab5c875c13150e3cd4