I. A. Ivanishko, V. G. Krotov, “Compactness of Embeddings of Sobolev Type on Metric Measure Spaces”, Mat. Zametki, 86:6 (2009), 829–844; Math. Notes, 86:6 (2009), 775

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Matematicheskie Zametki, 2009, Volume 86, Issue 6, Pages 829–844
DOI: https://doi.org/10.4213/mzm8526 (Mi mzm8526)

This article is cited in 18 scientific papers (total in 18 papers)

Compactness of Embeddings of Sobolev Type on Metric Measure Spaces

I. A. Ivanishko, V. G. Krotov

Belarusian State University

Full-text PDF (596 kB) Citations (18)

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DOI: https://doi.org/10.4213/mzm8526

Abstract: We establish conditions for the compactness of embeddings for some classes of functions on metric space with measure satisfying the duplication condition. These classes are defined in terms of the

$L^p$ -summability of maximal functions measuring local smoothness.

Keywords: embedding of Sobolev type, metric measure space, Hardy–Littlewood maximal function, Hölder class, Sobolev space, Borel measure, Lebesgue measure.

Received: 06.04.2009

English version:
Mathematical Notes, 2009, Volume 86, Issue 6, Pages 775–788
DOI: https://doi.org/10.1134/S0001434609110200

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: I. A. Ivanishko, V. G. Krotov, “Compactness of Embeddings of Sobolev Type on Metric Measure Spaces”, Mat. Zametki, 86:6 (2009), 829–844; Math. Notes, 86:6 (2009), 775–788

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8526

https://doi.org/10.4213/mzm8526

https://www.mathnet.ru/eng/mzm/v86/i6/p829

This publication is cited in the following 18 articles:

Nathan Wagner, Contemporary Mathematics, 792, Recent Developments in Harmonic Analysis and its Applications, 2024, 101
Mishko Mitkovski, Cody B. Stockdale, Nathan A. Wagner, Brett D. Wick, “Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications”, Complex Anal. Oper. Theory, 17:3 (2023)
N. N. Romanovskii, “Sobolev embedding theorems and their generalizations for maps defined on topological spaces with measures”, Moscow University Mathematics Bulletin, 77:1 (2022), 27–40
Nikolay A Torkhov, Leonid I Babak, Vadim A Budnyaev, Katerina V Kareva, Vadim A Novikov, “Conversion of the anomalous skin effect to the normal one in thin-film metallic microwave systems”, Phys. Scr., 97:9 (2022), 095809
N A Torkhov, A V Gradoboev, K N Orlova, A S Toropov, “Physical nature of size effects in TiAlNiAu/GaN ohmic contacts to AlGaN/GaN heteroepitaxial structures”, Semicond. Sci. Technol., 37:5 (2022), 055023
Torkhov N.A., Evstigneev M.P., Kokolov A.A., Babak L.I., “The Fractal Geometry of Tialniau Thin Film Metal System and Its Sheet Resistance (Lateral Size Effect)”, Symmetry-Basel, 13:12 (2021), 2391
Kukushkin M.V., “Note on the Equivalence of Special Norms on the Lebesgue Space”, Axioms, 10:2 (2021), 64
Torkhov N.A., Kokolov A.A., Babak I L., “Influence of the Surface Morphology of the Microwave Microstrip Line on Its Transmission Performance”, Semiconductors, 54:11 (2020), 1472–1477
Torkhov N.A., “Sheet Resistance of the Tialniau Thin-Film Metallization of Ohmic Contacts to Nitride Semiconductor Structures”, Semiconductors, 53:1 (2019), 28–36
Torkhov N.A., Babak L.I., Kokolov A.A., “The Influence of Algan/Gan Heteroepitaxial Structure Fractal Geometry on Size Effects in Microwave Characteristics of Algan/Gan Hemts”, Symmetry-Basel, 11:12 (2019), 1495
N. N. Romanovskiǐ, “Sobolev embedding theorems and generalizations for functions on a metric measure space”, Siberian Math. J., 59:1 (2018), 126–135
Dejun Luo, “The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients”, Stochastics, 90:3 (2018), 379
Torkhov N.A., Babak L.I., Kokolov A.A., Salnikov A.S., Dobush I.M., Novikov V.A., Ivonin I.V., “Nature of size effects in compact models of field effect transistors”, J. Appl. Phys., 119:9 (2016), 094505
N. N. Romanovskiǐ, “Embedding theorems and a variational problem for functions on a metric measure space”, Siberian Math. J., 55:3 (2014), 511–529
N. N. Romanovskiǐ, “Sobolev spaces on an arbitrary metric measure space: Compactness of embeddings”, Siberian Math. J., 54:2 (2013), 353–367
V. G. Krotov, “Criteria for compactness in $L^p$ -spaces, $p\geqslant0$ ”, Sb. Math., 203:7 (2012), 1045–1064
Veniamin G. Krotov, Springer Proceedings in Mathematics & Statistics, 25, Recent Advances in Harmonic Analysis and Applications, 2012, 197
Krotov V.G., “Quantitative form of the Luzin $C$ -property”, Ukrainian Math. J., 62:3 (2010), 441–451

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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