| 1. |
- Aksoy, A.G., et al.
(författare)
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Lipschitz-Orlicz Spaces and the Laplace Equation
- 1996
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 178:1, s. 81-101
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Tidskriftsartikel (refereegranskat)abstract
- Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (α, Lm) and Zygmund-Orlicz spaces Zyg (φ, Lm) and to the general function φ ϵ P instead of the power function φ(t)= tα. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces Lm (IRn). More general spaces δk(φ,X, q) are also considered.
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| 2. |
- Aksoy, A. G., et al.
(författare)
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Real interpolation and measure of weak noncompactness
- 1995
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 175:1, s. 5-12
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Tidskriftsartikel (refereegranskat)abstract
- Behavior of weak measures of noncompactness under real interpolation is investigated. It is shown that "convexity type" theorems hold true for weak measures of noncompactness.
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| 3. |
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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- Astashkin, Sergey, et al.
(författare)
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Isomorphic structure of Cesàro and Tandori spaces
- 2019
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Ingår i: Canadian Journal of Mathematics - Journal Canadien de Mathematiques. - : Cambridge University Press. - 0008-414X .- 1496-4279. ; 71:3, s. 501-532
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.
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| 9. |
- 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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| 10. |
- Astashkin, Sergey, et al.
(författare)
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Rademacher functions in Cesaro type spaces
- 2010
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 198:3, s. 235-247
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Tidskriftsartikel (refereegranskat)abstract
- The Rademacher sums are investigated in the Cesaro spaces Ces(p) (1 <= p <= infinity) and in the weighted Korenblyum-Krein-Levin spaces K-p,K-w on [0,1]. They span l(2) space in Ces(p) for any 1 <= p < infinity and in K-p,K-w if and only if the weight w is larger than t log(2)(p/2)(2/t) on (0,1). Moreover, the span of the Rademachers is not complemented in Ces(p) for any 1 <= p < infinity or in K-1,K-w for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l(2), this span is a complemented subspace in K-p,K-w.
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