Subdyadic square functions and applications to weighted harmonic analysis

David Beltran, Jonathan Bennett

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
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Abstract

Through the study of novel variants of the classical Littlewood–Paley–Stein g-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on ℝd satisfying regularity hypotheses adapted to fine (subdyadic) scales. In particular, this allows us to efficiently bound such multipliers by geometrically-defined maximal operators via general weighted L2 inequalities, in the spirit of a well-known conjecture of Stein. Our framework applies to solution operators for dispersive PDE, such as the time-dependent free Schrödinger equation, and other highly oscillatory convolution operators that fall well beyond the scope of the Calderón–Zygmund theory.
Original languageEnglish
Pages (from-to)72-99
Number of pages28
JournalAdvances in Mathematics
Volume307
Early online date22 Nov 2016
DOIs
Publication statusPublished - 5 Feb 2017

Keywords

  • Square functions
  • Fourier multipliers
  • Weighted inequalities
  • Oscillatory integrals

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