齐型空间上的变指标Herz空间
Herz space with variable exponent on spaces of homogeneous type

DOI: 10.7523/j.issn.2095-6134.2017.05.002

Keywords: Herz空间,变指标,齐型空间,块分解,有界性
Herz space,variable exponent,spaces of homogeneous type,block decomposition,boundedness

Full-Text   Cite this paper   Add to My Lib

Abstract:

摘要 引入一类齐型空间上的变指标Herz空间，并建立该空间的块分解.利用此分解得到一类次线性算子在上述变指标Herz空间中的一些有界性.

References

[1]	Harjulehto P, H？st？ P, Pere M. Variable exponent Lebesgue spaces on metric spaces:the Hardy-Littlewood maximal operator[J]. Real Anal Exchange, 2004, 30(1):87-104.
[2]	Liu Z, Zeng Y. The Herz spaces on spaces of homogeneous type and their applications[J]. Acta Math Sci Ser A Chin Ed, 1999,19:270-277.
[3]	Lu S, Yang D. The decomposition of weighted Herz space on R<sup>n</sup> and its applications[J]. Sci China Ser A-Math, 1995, 38:147-158.
[4]	Wang H. The decomposition for the Herz spaces[J]. Panamer Math J, 2015, 25:15-28.
[5]	Coifman R R, Weiss G. Extensions of Hardy spaces and their use in analysis[J].Bull Amer Math Soc, 1977, 83:569-645.
[6]	Hajlasz P, Koskela P. Sobolev met Poincare[J]. Mem Amer Math Soc, 2000,145(688):1-106.
[7]	Izuki M. Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization[J]. Anal Math, 2010, 36:33-50.
[8]	Almeida A, Hasanov J, Samko S. Maximal and potential operators in variable exponent Morrey spaces[J]. Georgian Math J, 2008, 15:195-208.
[9]	Kovác ik O, Rákosník J. On spaces L<sup>p(x)</sup> and W<sup>k,p(x)</sup>[J]. Czechoslovak Math J, 1991, 41:592-618.
[10]	Cruz-Uribe D, Fiorenza A. Variable Lebesgue spaces:foundations and harmonic analysis (applied and numerical harmonic analysis)[M]. Heidelberg:Springer, 2013.
[11]	Diening L, Harjulehto P, H？st？ P, et al. Lebesgue and Sobolev spaces with variable exponents[M]. Lecture Notes in Math, vol.2017.Heidelberg:Springer, 2011.

Full-Text