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