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Besov Spaces on Non-Homogeneous Martingales

In: Harmonic Analysis and Discrete Potential Theory

Author

Listed:
  • Chi Gu

    (Washington University, Department of Mathematics)

  • Mitchell Taibleson

    (Washington University, Department of Mathematics)

Abstract

Harmonic analysis on martingales has been studied in several papers in recent years. (See [C], [C-T1], [C-T2], [B-G-S], [K-P-T], [J], [U]). The work of Chao and Taibleson focused on discrete martingales. They derived a series of results on H p spaces including a characterization of H 1 by a “Hilbert transform” ([C], [C-T1]). This work was generalized in [K-P-T] and [C-T2] to the non-homogeneous case. Onneweer considered analysis on Vilenkin groups, which he studied by means of an extension of the method of homogeneous trees. In [O-S], Besov spaces on Vilenkin groups were introduced. We give a definition of Besov spaces on non-homogeneous trees, and discuss a few equivalent norms in this paper. In a later paper the first author will study operators on these spaces. Background and details for the construction and notation in this paper can be found in [K-P-T], [T2], and [T3].

Suggested Citation

  • Chi Gu & Mitchell Taibleson, 1992. "Besov Spaces on Non-Homogeneous Martingales," Springer Books, in: Massimo A. Picardello (ed.), Harmonic Analysis and Discrete Potential Theory, pages 69-84, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2323-3_6
    DOI: 10.1007/978-1-4899-2323-3_6
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