Geodesic
A semi-discrete Littlewood–Paley inequality
J. M. Wilson 1
1 Department of Mathematics University of Vermont Burlington, VT 05405, U.S.A.
Studia Mathematica, Tome 153 (2002) no. 3, pp. 207-233 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We apply a decomposition lemma of Uchiyama and results of the author to obtain good weighted Littlewood–Paley estimates for linear sums of functions satisfying reasonable decay, smoothness, and cancellation conditions. The heart of our application is a combinatorial trick treating $m$-fold dilates of dyadic cubes. We use our estimates to obtain new weighted inequalities for Bergman-type spaces defined on upper half-spaces in one and two parameters, extending earlier work of R. L. Wheeden and the author.
DOI : 10.4064/sm153-3-1
Keywords: apply decomposition lemma uchiyama results author obtain weighted littlewood paley estimates linear sums functions satisfying reasonable decay smoothness cancellation conditions heart application combinatorial trick treating m fold dilates dyadic cubes estimates obtain weighted inequalities bergman type spaces defined upper half spaces parameters extending earlier work wheeden author

J. M. Wilson  1

1 Department of Mathematics University of Vermont Burlington, VT 05405, U.S.A. 
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J. M. Wilson. A semi-discrete Littlewood–Paley inequality. Studia Mathematica, Tome 153 (2002) no. 3, pp. 207-233. doi: 10.4064/sm153-3-1

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