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On a geometric inequality related to fractional integration
- Publication Year :
- 2016
- Publisher :
- arXiv, 2016.
-
Abstract
- In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear integral, we establish this new kind of geometric inequalities with bilinear form and multilinear form in more general settings. Moreover, in some cases we also find the best constants and optimisers for these geometric inequalities on Euclidean spaces with Lebesgue measure settings with $L^p$ bounds.
- Subjects :
- Multilinear map
Pure mathematics
Mathematics::Functional Analysis
Partial differential equation
Lebesgue measure
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematics::Classical Analysis and ODEs
Bilinear form
01 natural sciences
Sobolev inequality
Functional Analysis (math.FA)
Mathematics - Functional Analysis
symbols.namesake
Multilinear form
Fourier analysis
0103 physical sciences
Euclidean geometry
symbols
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Analysis
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....e8f6f8327619d56ab2dd2456c2278c40
- Full Text :
- https://doi.org/10.48550/arxiv.1606.05206