| 1. |
- Asekritova, Irina, et al.
(författare)
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Lions-Peetre Reiteration Formulas for Triples and Their Application
- 2001
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 145:3, s. 219-254
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Tidskriftsartikel (refereegranskat)abstract
- We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted Lp-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein–Weiss interpolation theorem known for Lp(μ)-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.
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| 2. |
- Astashin, S. V., et al.
(författare)
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On interpolation in Lp spaces
- 2003
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Ingår i: Mathematical notes of the Academy of Sciences of the USSR. - 0001-4346 .- 1573-8876. ; 74:5-6, s. 734-739
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Astashkin, Sergey, et al.
(författare)
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Cesaro function spaces fail the fixed point property
- 2008
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 136:12, s. 4289-4294
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Tidskriftsartikel (refereegranskat)abstract
- The Cesaro sequence spaces ces(p), 1 < p < infinity, are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesaro function spaces Ces(p) on both [0, 1] and [0, infinity) for 1 < p < infinity are not reflexive and they fail to have the fixed point property.
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| 4. |
- Astashkin, Sergey, et al.
(författare)
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Interpolation between L1 and Lp, 1
- 2004
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 132:10, s. 2929-2938
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Tidskriftsartikel (refereegranskat)abstract
- The main result of this paper is that if $X$ is an interpolation rearrangement invariant space on $[0,1]$ between $L_1$ and $L_\infty$, for which the Boyd index $\alpha(X)>1/p$, $1
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| 5. |
- Astashkin, S., et al.
(författare)
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On interpolation in Lp-spaces
- 2003
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Ingår i: Mathematical notes of the Academy of Sciences of the USSR. - : Steklov Mathematical Institute. - 0001-4346 .- 1573-8876. ; 74:5, s. 782-786
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Tidskriftsartikel (refereegranskat)
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| 6. |
- Astashkin, Sergey, et al.
(författare)
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Structure of Cesaro function spaces
- 2009
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Ingår i: Indagationes mathematicae. - 0019-3577 .- 1872-6100. ; 20:3, s. 329-379
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Tidskriftsartikel (refereegranskat)abstract
- The structure of the Cesàro function spaces Cesp on both [0,1] and [0, ∞) for 1 < p ≤ ∞ is investigated. We find their dual spaces, which equivalent norms have different description on [0, 1] and [0, ∞).The spaces Cesp for 1 < p < ∞ are not reflexive but strictly convex. They are not isomorphic to any Lq space with 1 ≤ q ≤ ∞. They have "near zero" complemented subspaces isomorphic to lp and "in the middle" contain an asymptotically isometric copy of l1 and also a copy of L1[0, 1]. They do not have Dunford-Pettis property but they do have the weak Banach-Saks property. Cesàro function spaces on [0, 1] and [0, ∞) are isomorphic for 1 < p ≤ ∞. Moreover, we give characterizations in terms of p and q when Cesp[0, 1] contains an isomorphic copy of lq.
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| 7. |
- Astashkin, Sergey, et al.
(författare)
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Ultrasymmetric Orlicz spaces
- 2008
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 347:1, s. 273-285
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Tidskriftsartikel (refereegranskat)abstract
- It is proved that ultrasymmetric reflexive Orlicz spaces can be described exactly as all those Orlicz spaces which can be written as some Lorentz spaces. This description is an answer to the problem posed by Pustylnik in [E. Pustylnik, Ultrasymmetric spaces, J. London Math. Soc. (2) 68 (1) (2003) 165-182]. On the other hand, the Lorentz-Orlicz spaces with non-trivial indices of their fundamental functions are ultrasymmetric.
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| 8. |
- Astashkin, Sergey V., et al.
(författare)
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Multiplicator space and complemented subspaces of rearrangement invariant space
- 2003
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; 202:1, s. 247-276
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Tidskriftsartikel (refereegranskat)abstract
- We show that the multiplicator space M(X) of an rearrangement invariant (r.i.) space X on [0, 1] and the nice part N0 (X) of X, that is, the set of all a ∈ X for which the subspaces generated by sequences of dilations and translations of a are uniformly complemented, coincide when the space X is separable. In the general case, the nice part is larger than the multiplicator space. Several examples of descriptions of M(X) and N0(X) for concrete X are presented
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| 9. |
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| 10. |
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