Self-affine measures that are $L^p$-improving

Kathryn E. Hare. "Self-affine measures that are $L^{p}$-improving." Colloquium Mathematicae 139.2 (2015): 229-243. <http://eudml.org/doc/284351>.

@article{KathrynE2015,
abstract = {A measure is called $L^\{p\}$-improving if it acts by convolution as a bounded operator from $L^\{q\}$ to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are $L^\{p\}$-improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be $L^\{p\}$-improving.},
author = {Kathryn E. Hare},
journal = {Colloquium Mathematicae},
keywords = {-improving; self-affine; self-similar},
language = {eng},
number = {2},
pages = {229-243},
title = {Self-affine measures that are $L^\{p\}$-improving},
url = {http://eudml.org/doc/284351},
volume = {139},
year = {2015},
}

TY - JOUR
AU - Kathryn E. Hare
TI - Self-affine measures that are $L^{p}$-improving
JO - Colloquium Mathematicae
PY - 2015
VL - 139
IS - 2
SP - 229
EP - 243
AB - A measure is called $L^{p}$-improving if it acts by convolution as a bounded operator from $L^{q}$ to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are $L^{p}$-improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be $L^{p}$-improving.
LA - eng
KW - -improving; self-affine; self-similar
UR - http://eudml.org/doc/284351
ER -