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

  • JI LI (a1)
Abstract
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.

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[3]R. R. Coifman and G. Weiss , Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, 242 (Springer, Berlin, 1971).

[7]M. Frazier and B. Jawerth , ‘A discrete transform and decomposition of distribution spaces’, J. Funct. Anal. 93 (1990), 34170.

[8]J. García-Cuerva and J. M. Martell , ‘Wavelet characterization of weighted spaces’, J. Geom. Anal. 11 (2001), 241264.

[9]J. García-Cuerva and J. L. Rubio de Francia , Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, 116 (North-Holland, Amsterdam, 1985).

[16]Y. S. Han , D. Müller and D. Yang , ‘A theory of Besov and Triebel–Lizorkin spaces on metric measure spaces modeled on Carnot–Carathéodory spaces’, Abstr. Appl. Anal. (2008), Article ID 893409.

[18]Y. S. Han and D. Yang , ‘Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces’, Studia Math. 156 (2003), 6797.

[19]R. A. Macías and C. Segovia , ‘Lipschitz functions on spaces of homogeneous type’, Adv. Math. 33 (1979), 257270.

[20]B. Muckenhoupt , ‘Weighted norm inequalities for the Hardy maximal functions’, Trans. Amer. Math. Soc. 165 (1972), 207226.

[22]D. Yang , ‘Some new Triebel–Lizorkin spaces on spaces of homogeneous type and their frame characterizations’, Sci. China Ser. A 48 (2005), 1239.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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