Geodesic
On Spaces Associated with Weighted Ces\`aro and Copson Spaces
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 443-450.

Voir la notice de l'article provenant de la source Math-Net.Ru

A description of spaces associated with weighted Cesàro and Copson spaces is presented. The answer is given in the form of sharp formulas for functionals equivalent to the norms of the corresponding associated spaces. All cases of the summation parameter and weight functions are studied.
Keywords: Cesàro space, Copson space, associated space. 
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V. D. Stepanov. On Spaces Associated with Weighted Ces\`aro and Copson Spaces. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 443-450. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a10/

[1] G. Bennett, Factorizing the Classical Inequalities, Mem. Amer. Math. Soc., 120, no. 576, Amer. Math. Soc., Providence, RI, 1996 | MR

[2] S. V. Astashkin, L. Maligranda, “Structure of Cesàro function spaces: a survey”, Function Spaces X, Banach Center Publ., 102, Polish Acad. Sci. Inst. Math., Warsaw, 2014, 13–40 | DOI | MR | Zbl

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

[4] C. Bennett, R. Sharpley, Interpolation of Operators, Academic Press, Boston, MA, 1988 | MR | Zbl

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

[6] B. D. Hassard, D. A. Hussein, “On Cesàro function spaces”, Tamkang J. Math., 4 (1973), 19–25 | MR | Zbl

[7] A. Kaminska, D. Kubiak, “On the dual of Cesàro function space”, Nonlinear Anal., 75:5 (2012), 2760–2773 | DOI | MR | Zbl

[8] G. Sinnamon, “Transferring monotonicity in weighted norm inequalities”, Collect. Math., 54:2 (2003), 181–216 | MR | Zbl

[9] M. Carro, A. Gogatishvili, J. Martin, L. Pick, “Weighted inequalities involving two Hardy operators with applications to embeddings of function spaces”, J. Operator Theory, 59:2 (2008), 309–332 | MR | Zbl

[10] E. Sawyer, “Boundedness of classical operators on classical Lorentz spaces”, Studia Math., 96:2 (1990), 145–158 | DOI | MR | Zbl

[11] V. D. Stepanov, “The weighted Hardy's inequality for nonincreasing functions”, Trans. Amer. Math. Soc., 338:1 (1993), 173–186 | MR | Zbl

[12] A. Gogatishvili, V. D. Stepanov, “Reduktsionnye teoremy dlya vesovykh integralnykh neravenstv na konuse monotonnykh funktsii”, UMN, 68:4 (412) (2013), 3–68 | DOI | MR | Zbl

[13] G. Sinnamon, “Hardy's inequality and monotonicity”, Function Spaces, Differential Operators and Nonlinear Analysis, Conf. Proc., eds. P. Drábek, J. Rákosnik, Math. Inst. Acad. Sci. Czech Repub., Praha, 2005, 292–310 www.obalkyknih.cz/view?isbn=8085823527

[14] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1976 | MR | Zbl

[15] S. V. Astashkin, L. Maligranda, “Structure of Cesàro function spaces”, Indag. Math. (N.S.), 20:3 (2009), 329–379 | DOI | MR | Zbl

[16] S. V. Astashkin, E. M. Semenov, “Ob odnom svoistve simmetrichnykh prostranstv, vtoroe assotsiirovannoe prostranstvo k kotorym neseparabelno”, Matem. zametki, 107:1 (2020), 11–22 | DOI | MR | Zbl

[17] M. L. Goldman, P. P. Zabreiko, “Optimalnoe vosstanovlenie banakhova funktsionalnogo prostranstva po konusu neotritsatelnykh funktsii”, Funktsionalnye prostranstva i smezhnye voprosy analiza, Trudy MIAN, 284, MAIK «Nauka/Interperiodika», M., 2014, 142–156 | DOI

[18] V. D. Stepanov, “Ob optimalnykh prostranstvakh Banakha, soderzhaschikh vesovoi konus monotonnykh ili kvazivognutykh funktsii”, Matem. zametki, 98:6 (2015), 907–922 | DOI | MR | Zbl