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Matematicheskie Zametki, 2006, Volume 80, Issue 6, Pages 803–813
DOI: https://doi.org/10.4213/mzm3358 (Mi mzm3358) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Interpolation properties of scales of Banach spaces

Yu. N. Bykova, V. I. Ovchinnikovb

a Kursk State University
b Voronezh State University
Full-text PDF (404 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm3358
Abstract: It is shown that any interpolation scales joining weight spaces Lp or similar spaces have many remarkable properties. Not only are such scales intrinsically interpolation scales, but an analog of the Arazy–Cwikel theorem describing interpolation spaces between the spaces from the scale is valid.
Received: 27.07.2005
Revised: 25.01.2006
English version:
Mathematical Notes, 2006, Volume 80, Issue 6, Pages 761–769
DOI: https://doi.org/10.1007/s11006-006-0199-z
Bibliographic databases:
UDC: 517.982
Language: Russian
Citation: Yu. N. Bykov, V. I. Ovchinnikov, “Interpolation properties of scales of Banach spaces”, Mat. Zametki, 80:6 (2006), 803–813; Math. Notes, 80:6 (2006), 761–769
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3358
  • https://www.mathnet.ru/eng/mzm/v80/i6/p803
    • This publication is cited in the following 4 articles:
    1. Sergey V. Astashkin, Michael Cwikel, Per G. Nilsson, “Arazy–Cwikel and Calderón–Mityagin type properties of the couples $(\ell ^{p},\ell ^{q})$, $0\le p<q\le \infty $”, Annali di Matematica, 202:4 (2023), 1643  crossref
    2. Sergey V. Astashkin, Per G. Nilsson, “Arazy-Cwikel property for quasi-banach couples”, Positivity, 26:4 (2022)  crossref
    3. Kussainova L., Ospanova A., “Interpolation Theorems For Weighted Sobolev Spaces”, World Congress on Engineering, Wce 2015, Vol i, Lecture Notes in Engineering and Computer Science, eds. Ao S., Gelman L., Hukins D., Hunter A., Korsunsky A., Int Assoc Engineers-Iaeng, 2015, 25–28  isi
    4. Gogatishvili A., Ovchinnikov V. I., “Interpolation orbits and optimal Sobolev's embeddings”, J. Funct. Anal., 253:1 (2007), 1–17  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:51
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