A convolution property of some measures with self-similar fractal support

Denise Szecsei. "A convolution property of some measures with self-similar fractal support." Colloquium Mathematicae 109.2 (2007): 171-177. <http://eudml.org/doc/283835>.

@article{DeniseSzecsei2007,
abstract = {We define a class of measures having the following properties: (1) the measures are supported on self-similar fractal subsets of the unit cube $I^\{M\} = [0,1)^\{M\}$, with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on $I^\{M\}$; (3) the measures have the convolution property that $μ∗ L^\{p\} ⊆ L^\{p+ε\}$ for some ε = ε(p) > 0 and all p ∈ (1,∞). We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then $μ ∗ L^\{p\} ⊆ L^\{q\}$ for any measure μ in our class.},
author = {Denise Szecsei},
journal = {Colloquium Mathematicae},
keywords = {singular measures; convolution},
language = {eng},
number = {2},
pages = {171-177},
title = {A convolution property of some measures with self-similar fractal support},
url = {http://eudml.org/doc/283835},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Denise Szecsei
TI - A convolution property of some measures with self-similar fractal support
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 2
SP - 171
EP - 177
AB - We define a class of measures having the following properties: (1) the measures are supported on self-similar fractal subsets of the unit cube $I^{M} = [0,1)^{M}$, with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on $I^{M}$; (3) the measures have the convolution property that $μ∗ L^{p} ⊆ L^{p+ε}$ for some ε = ε(p) > 0 and all p ∈ (1,∞). We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then $μ ∗ L^{p} ⊆ L^{q}$ for any measure μ in our class.
LA - eng
KW - singular measures; convolution
UR - http://eudml.org/doc/283835
ER -