Fourier multipliers and weak differential subordination of martingales in UMD Banach spaces

Ivan Yaroslavtsev

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
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Abstract

We introduce the notion of weak differential subordination for martingales, and show that a Banach space X is UMD if and only if for all p ∈ (1, ∞) and all purely discontinuous X-valued martingales M and N such that N is weakly differentially subordinated to M, one has the estimate E || N ||p ≤ CpE|| M ||p. As a corollary we derive a sharp estimate for the norms of a broad class of even Fourier multipliers, which includes e.g. the second order Riesz transforms.

Original languageEnglish
Pages (from-to)269-301
Number of pages33
JournalStudia Mathematica
Volume243
Issue number3
DOIs
Publication statusPublished - 2018

Keywords

  • Burkholder function
  • Differential subordination
  • Fourier multipliers
  • Hilbert transform
  • Lévy process
  • Purely discontinuous martingales
  • Sharp estimates
  • Stochastic integration
  • UMD Banach spaces
  • Weak differential subordination

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  • Martingales and stochastic calculus in Banach spaces

    Yaroslavtsev, I., 1 Mar 2019, 302 p.

    Research output: ThesisDissertation (TU Delft)

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