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Abstract Cesàro Spaces. Optimal Range
- 作者:Karol Le?nik ; Lech Maligranda
- 关键词:46E30 ; 46B20 ; 46B42 ; Cesàro function spaces ; Cesàro operator ; maximal operator ; Banach ideal spaces ; symmetric spaces ; optimal domain ; optimal range
- 刊名:Integral Equations and Operator Theory
- 出版年:2015
- 出版时间:February 2015
- 年:2015
- 卷:81
- 期:2
- 页码:227-235
- 全文大小:231 KB
- 参考文献:1. Astashkin S.V., Maligranda L.: Structure of Cesàro function spaces. Indag. Math. (N.S.) 20(3), 329-79 (2009) CrossRef
2. Bennett C., Sharpley R.: Interpolation of Operators. Academic Press, Boston (1988) 3. Delgado O., Soria J.: Optimal domain for the Hardy operator. J. Funct. Anal. 244(1), 119-33 (2007) CrossRef 4. Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Nauka, Moscow (1977) (Russian); English transl. Pergamon Press, Oxford-Elmsford, New York (1982) 5. Krein S.G., Petunin Yu.I., Semenov E.M.: Interpolation of Linear Operators. American Mathematical Society, Providence (1982) 6. Le?nik, K., Maligranda, L.: On abstract Cesàro spaces. Duality. J. Math. Anal. Appl. (2015). doi:10.1016/j.jmaa.2014.11.023 7. Lindenstrauss J., Tzafriri L.: Classical Banach Spaces, II. Function Spaces. Springer, Berlin (1979) CrossRef 8. Maligranda L.: Orlicz Spaces and Interpolation. Seminars in Mathematics 5. University of Campinas, Campinas (1989) 9. Mizuta Y., Nekvinda A., Shimomura T.: Hardy averaging operator on generalized Banach function spaces and duality. Z. Anal. Anwend. 32(2), 233-55 (2013) CrossRef 10. Nekvinda A., Pick L.: Optimal estimates for the Hardy averaging operator. Math. Nachr. 283(2), 262-71 (2010) CrossRef 11. Nekvinda A., Pick L.: Duals of optimal spaces for the Hardy averaging operator. Z. Anal. Anwend. 30(4), 435-56 (2011) CrossRef
- 刊物类别:Mathematics and Statistics
- 刊物主题:Mathematics
Analysis
- 出版者:Birkh盲user Basel
- ISSN:1420-8989
文摘
Abstract Cesàro spaces are investigated from the optimal domain and optimal range point of view. There is a big difference between the cases on [0, ? and on [0, 1], as we can see in Theorem 1. Moreover, we present an improvement of Hardy’s inequality on [0, 1] which plays an important role in these considerations.
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