Geodesic
Non-compact Littlewood–Paley theory for non-doubling measures
Michael Wilson1
1Department of Mathematics University of Vermont Burlington, VT 05405, U.S.A.
Studia Mathematica, Tome 183 (2007) no. 3, pp. 197-223
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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.
DOI : 10.4064/sm183-3-1
Keywords: prove weighted littlewood paley inequalities linear sums functions satisfying mild decay smoothness cancelation conditions prove these general regular measure spaces which underlying measure assumed satisfy doubling condition result generalizes earlier result author proved mathbb lebesgue measure proof makes essential technique random dyadic grids due nazarov treil volberg

Michael Wilson  1

1 Department of Mathematics University of Vermont Burlington, VT 05405, U.S.A. 
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Michael Wilson. Non-compact Littlewood–Paley theory for
 non-doubling measures. Studia Mathematica, Tome 183 (2007) no. 3, pp. 197-223. doi: 10.4064/sm183-3-1

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