Geodesic
On the associated spaces of the weighted altered Ces\`aro space
Eurasian mathematical journal, Tome 15 (2024) no. 1, pp. 55-64.

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We study weighted altered Cesàro space $\mathrm{Ch}_{\infty,w}(I)$, which is a non-ideal enlargement of the usual Cesàro space. We prove the connection of this space with one weighted Sobolev space of the first order on real line and give characterizations of associate spaces of this space. 
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D. V. Prokhorov. On the associated spaces of the weighted altered Ces\`aro space. Eurasian mathematical journal, Tome 15 (2024) no. 1, pp. 55-64. http://geodesic.mathdoc.fr/item/EMJ_2024_15_1_a4/

[1] S. V. Astashkin, L. Maligranda, “Structure of Cesàro function spaces: a survey”, Function Spaces X, Proc. Int. Conf et al. (Poznan 2012), Banach Center Publications, 102, eds. H. Hudzik et al., 2014, 13–40 | DOI | MR | Zbl

[2] C. Bennett, R. Sharpley, Interpolation of operators, Academic Press, Inc, Boston, MA etc., 1988 | MR | Zbl

[3] A. Kaminska, D. Kubiak, “On the dual of Cesàro function space”, Nonlinear Anal., 75 (2012), 2760–2773 | DOI | MR | Zbl

[4] A. Kalybay, R. Oinarov, “Boundedness of Riemann Liouville operator from weighted Sobolev space to weighted Lebesgue space”, J. Eurasian Math., 12:1 (2021), 39–48 | DOI | MR | Zbl

[5] G. Leoni, A first course in Sobolev spaces, American Mathematical Society, Providence, RI, 2009 | MR | Zbl

[6] K. Leśnik, L. Maligranda, “Abstract Cesàro spaces. Duality”, J. Math. Anal. Appl., 424 (2015), 932–951 | DOI | MR | Zbl

[7] K. T. Mynbaev, M. O. Otelbaev, Weighted function spaces and the spectrum of differential operators, Nauka, M., 1988 (in Russian) | MR

[8] R. Oinarov, “On weighted norm inequalities with three weights”, J. London Math. Soc., 48:2 (1993), 103–116 | DOI | MR | Zbl

[9] D. V. Prokhorov, “On the associate spaces for altered Cesàro space”, Anal. Math., 48 (2022), 1169–1183 | DOI | MR | Zbl

[10] D. V. Prokhorov, “On the dual spaces for weighted altered Cesàro and Copson spaces”, J. Math. Anal. Appl., 514:2 (2022), 126325 | DOI | MR | Zbl

[11] D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “On associate spaces of weighted Sobolev space on the real line”, Math. Nachr., 290 (2017), 890–912 | DOI | MR | Zbl

[12] D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line”, Russian Math. Surveys, 74:6 (2019), 1075–1115 | DOI | MR | Zbl

[13] W. Rudin, Real and complex analysis, Third ed., McGraw-Hill, New York, 1987 | MR | Zbl

[14] V. D. Stepanov, “On Cesàro and Copson type function spaces. Reflexivity”, J. Math. Anal. Appl., 507:1 (2022), 125764 | DOI | MR | Zbl

[15] V. D. Stepanov, “On spaces associated with weighted Cesàro and Copson spaces”, Math. Notes, 111:3 (2022), 470–477 | DOI | MR | Zbl