Atomic decomposition of Hardy spaces and characterization of BMO via Banach function spaces

详细信息    查看全文

• 作者：Kwok-Pun Ho (1) vkpho@ied.edu.hk
• 刊名：Analysis Mathematica
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：38
• 期：3
• 页码：173-185
• 全文大小：183.2 KB
• 参考文献：1. H. Aoyama, Lebesgue spaces with variable exponent on a probability space, Hiroshima Math. J., 39(2009), 207–216.
  2. C. Bennett and R. Sharpley, Interpolations of operators, Academic Press (New York, 1988).
  3. D. Boyd Indices of function spaces and their relationship to interpolation, Canad. J. Math., 21(1969), 1245–1254.
  4. D. Cruz-Uribe, L. Diening, and A. A. Fiorenza, A new proof of the boundedness of maximal operators on variable Lebesgue spaces, Boll. Unione Mat. Ital., 2(1)(2009), 151–173.
  5. L. Diening, Maximal function on Orlicz-Musielak spaces and generalized Lebesgue space, Bull. Sci. Math., 129(2005), 657–700.
  6. L. Diening, P. Harjulehto, P. H茫st玫, Y. Mizuta, and T. Shimomura, Maximal functions in variable exponent spaces: limiting cases of the exponent, Ann. Acad. Sci. Fenn. Math., 34(2009), 503–522.
  7. K.-P. Ho, Characterization of BMO in terms of rearrangement-invariant Banach function spaces, Expo. Math., 27(2009), 363–372.
  8. K.-P. Ho, Littlewood-Paley spaces, Math. Scand., 108(2011), 77–102.
  9. K.-P. Ho, Characterizations of BMO by A p weights and P-convexity, Hiroshima Math. J., 41(2011), 153–165.
  10. K.-P. Ho, Generalized Boyd’s indices and applications Analysis (Munich), accepted.
  11. M. Izuki, Boundedness of commutators on Herz spaces with variable exponent, Rend. Circ. Mat. Palermo (2), 59(2010), 199–213.
  12. O. Kov谩čik and J. R谩kosn铆k, On spaces L p(路) and W k,p(路), Czechoslovak Math. J., 41(1991), 592–618.
  13. A. Lerner and S. Ombrosi, A boundedness criterion for general maximal operators, Publ. Mat., 54(2010), 53–71.
  14. J. Lukeš, L. Pick, and D. Pokorn媒, On geometric properties of the spaces L p(x), Rev. Mat. Comput., 24(2011), 115–130.
  15. E. Stein, Harmonic Analysis, Princeton University Press (Princeton, 1993).
• 作者单位：1. Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10, Lo Ping Road, Tai Po, Hong Kong, China
• ISSN：1588-273X

文摘

An atomic decomposition of Hardy spaces by atoms associated with Banach function space is developed. Inspired by these decompositions, a criterion on a general Banach function space is introduced so that the characterization of BMO by using that Banach function space is valid.