Journal of the Australian Mathematical Society

Research Article

ATOMIC DECOMPOSITION OF WEIGHTED TRIEBEL–LIZORKIN SPACES ON SPACES OF HOMOGENEOUS TYPE

JI LIa1

a1 Department of Mathematics, Sun Yat-sen University, Guangzhou, PR China (email: liji6@mail.sysu.edu.cn)

Abstract

We obtain an atomic decomposition for weighted Triebel–Lizorkin spaces on spaces of homogeneous type, using the area function, the discrete Calderón reproducing formula and discrete sequence spaces.

(Received June 14 2009)

(Accepted September 14 2010)

(Online publication January 25 2011)

2010 Mathematics subject classification

  • primary 42B35; secondary 42B20;
  • 46E

Keywords and phrases

  • weighted Triebel–Lizorkin spaces;
  • atomic decomposition;
  • Calderón reproducing formula;
  • spaces of homogeneous type

Footnotes

The author is supported by the Young Faculty Career Start Program (Grant No. 34000-3126172) and by NNSF of China (Grant No. 11001275).