Non-compact Littlewood–Paley theory for
non-doubling measures
Studia Mathematica, Tome 183 (2007) no. 3, pp. 197-223
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Michael Wilson 1
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
@article{10_4064_sm183_3_1,
author = {Michael Wilson},
title = {Non-compact {Littlewood{\textendash}Paley} theory for
non-doubling measures},
journal = {Studia Mathematica},
pages = {197--223},
year = {2007},
volume = {183},
number = {3},
doi = {10.4064/sm183-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm183-3-1/}
}
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