$L^p$-improving properties of measures of positive energy dimension

Kathryn E. Hare, and Maria Roginskaya. "$L^{p}$-improving properties of measures of positive energy dimension." Colloquium Mathematicae 102.1 (2005): 73-86. <http://eudml.org/doc/283473>.

@article{KathrynE2005,
abstract = {A measure is called $L^\{p\}$-improving if it acts by convolution as a bounded operator from $L^\{p\}$ to $L^\{q\}$ for some q > p. Positive measures which are $L^\{p\}$-improving are known to have positive Hausdorff dimension. We extend this result to complex $L^\{p\}$-improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of $L^\{p\}$-functions.},
author = {Kathryn E. Hare, Maria Roginskaya},
journal = {Colloquium Mathematicae},
keywords = {-improving measure; energy dimension; Hausdorff dimension; Lipschitz classes},
language = {eng},
number = {1},
pages = {73-86},
title = {$L^\{p\}$-improving properties of measures of positive energy dimension},
url = {http://eudml.org/doc/283473},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Kathryn E. Hare
AU - Maria Roginskaya
TI - $L^{p}$-improving properties of measures of positive energy dimension
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 73
EP - 86
AB - A measure is called $L^{p}$-improving if it acts by convolution as a bounded operator from $L^{p}$ to $L^{q}$ for some q > p. Positive measures which are $L^{p}$-improving are known to have positive Hausdorff dimension. We extend this result to complex $L^{p}$-improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of $L^{p}$-functions.
LA - eng
KW - -improving measure; energy dimension; Hausdorff dimension; Lipschitz classes
UR - http://eudml.org/doc/283473
ER -