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

• Autorzy: Michael Wilson
• Języki publikacji: EN

Abstrakty

EN

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 $ℝ^{d}$ with Lebesgue measure. Our proof makes essential use of the technique of random dyadic grids, due to Nazarov, Treil, and Volberg.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 183
• Numer: 3
• Strony: 197-223

Daty

wydano

2007

Twórcy

autor

Michael Wilson

• Department of Mathematics, University of Vermont, Burlington, VT 05405, U.S.A.

Identyfikatory

DOI

10.4064/sm183-3-1