Subdyadic square functions and applications to weighted harmonic analysis

David Beltran, Jonathan Bennett

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6 Citations (Scopus)
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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
Early online date22 Nov 2016
Publication statusPublished - 5 Feb 2017


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


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