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

Michael Wilson. "Non-compact Littlewood-Paley theory for non-doubling measures." Studia Mathematica 183.3 (2007): 197-223. <http://eudml.org/doc/284823>.

@article{MichaelWilson2007,
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 $ℝ^\{d\}$ with Lebesgue measure. Our proof makes essential use of the technique of random dyadic grids, due to Nazarov, Treil, and Volberg.},
author = {Michael Wilson},
journal = {Studia Mathematica},
keywords = {Littlewood-Paley theory; weighted norm inequalities},
language = {eng},
number = {3},
pages = {197-223},
title = {Non-compact Littlewood-Paley theory for non-doubling measures},
url = {http://eudml.org/doc/284823},
volume = {183},
year = {2007},
}

TY - JOUR
AU - Michael Wilson
TI - Non-compact Littlewood-Paley theory for non-doubling measures
JO - Studia Mathematica
PY - 2007
VL - 183
IS - 3
SP - 197
EP - 223
AB - 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.
LA - eng
KW - Littlewood-Paley theory; weighted norm inequalities
UR - http://eudml.org/doc/284823
ER -