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- Asekritova, Irina, et al.
(författare)
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Distribution and Rearranement Estimates of the Maximal Functions and Interpolation
- 1997
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Ingår i: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 124:2, s. 107-132
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Tidskriftsartikel (refereegranskat)abstract
- There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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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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| 7. |
- Asekritova, Irina, et al.
(författare)
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Real Interpolation of Vector-Valued Spaces in Non-Diagonal Case
- 2004
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 133:6, s. 1665-1675
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the formula where and is correct under the restrictions and It is also true if we suppose that and the spaces are functional Banach or quasi-Banach lattices on the same measure space
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| 9. |
- Asekritova, Irina, et al.
(författare)
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The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV)
- 2010
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1406-0086 .- 2228-0685 .- 1736-6046 .- 1736-7530. ; 59:1, s. 29-33
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be a rectangle in R2. A new algorithm for the construction of a near-minimizer for the couple (L2(Ω), BV(Ω)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f ∈ L2(Ω).
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