A+ CATEGORY SCIENTIFIC UNIT

Non-compact Littlewood–Paley theory for non-doubling measures

Volume 183 / 2007

Michael Wilson Studia Mathematica 183 (2007), 197-223 MSC: Primary 42B25. DOI: 10.4064/sm183-3-1

Abstract

We prove weighted Littlewood–Paley inequalities for linear sums of functions satisfying mild decay, smoothness, and cancelation conditions. We prove these for general “regular” measure spaces, in which the underlying measure is not assumed to satisfy any doubling condition. Our result generalizes an earlier result of the author, proved on ${{{\mathbb R}}^d}$ with Lebesgue measure. Our proof makes essential use of the technique of random dyadic grids, due to Nazarov, Treil, and Volberg.

Authors

  • Michael WilsonDepartment of Mathematics
    University of Vermont
    Burlington, VT 05405, U.S.A.
    e-mail

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