| 1. |
- Larsson, Leo, et al.
(författare)
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An extension of the Landau and Levin-Steckin inequalities
- 2004
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Ingår i: Acta Scientarum Mathematicarum. - 0001-6969. ; 70:1-2, s. 25-34
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Tidskriftsartikel (refereegranskat)abstract
- The authors prove an inequality for sums, which generalizes both Landau's sharpening of Carlson's inequality and the corresponding complementary result by Levin and Ste\v{c}kin. The inequality is optimal, in the sense that necessary and sufficient conditions on the parameters for which the inequality holds are given. In some cases, sharp constants are obtained, also in situations not covered by the classical results.
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| 2. |
- Larsson, Leo, et al.
(författare)
-
Carlson type inequalities for finite sums and integrals on bounded intervals
- 2005
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Ingår i: Bulletin of the Australian Mathematical Society. - 0004-9727 .- 1755-1633. ; 71:2, s. 275-284
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Tidskriftsartikel (refereegranskat)abstract
- We investigate Carlson type inequalities for finite sums, that is, inequalities of the form ∑mk=1ak < C (∑mk=1ka1akr+1) μ(∑mk=1ka2akr+1)λ, to hold for some constant C independent of the finite, non-zero set a1,⋯,am of non-negative numbers. We find constants C which are strictly smaller than the sharp constants in the corresponding infinite series case. Moreover, corresponding results for integrals over bounded intervals are given and a case with any finite number of factors on the right-hand side is proved
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| 3. |
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| 4. |
- Larsson, Leo, et al.
(författare)
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Carlson's inequality and interpolation
- 2006
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Ingår i: Proceedings of the Estonian Academy of Sciences. - 1406-0086 .- 2228-0685. ; 55:3, s. 182-188
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Tidskriftsartikel (refereegranskat)abstract
- In this survey, we explain and discuss some recent results concerning the close connection between Carlson type inequalities and interpolation theory. In particular, we point out that a fairly general Carlson type inequality can be used to extend the usefulness of the Gustavsson-Peetre $\langle·\rangle_\phi$ interpolation method
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| 5. |
- Larsson, Leo, et al.
(författare)
-
Carlson's inequality and interpolation
- 2006
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Ingår i: Proc. Estonian Acad. Sci. Phys. Math.. ; :03, s. 182-188
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 6. |
- Larsson, Leo, et al.
(författare)
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Multiplicative inequalities of Carlson type and interpolation
- 2006
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Collecting all the results on the particular types of inequalities, the coverage of this book is unique among textbooks in the literature. The book focuses on the historical development of the Carlson inequalities and their many generalizations and variations. As well as almost all known results concerning these inequalities and all known proof techniques, a number of open questions suitable for further research are considered. Two chapters are devoted to clarifying the close connection between interpolation theory and this type of inequality. Other applications are also included, in addition to a historical note on Fritz Carlson himself.
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