Journal article
A convolution property of some measures with self-similar fractal support
Colloquium Mathematicum, Vol.109(2), pp.171-177
2007
DOI: 10.4064/cm109-2-1
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 IM=[0,1)M, with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on IM; (3) the measures have the convolution property that μ∗Lp⊆Lp+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∗Lp⊆Lq for any measure μ in our class.
Details
- Title: Subtitle
- A convolution property of some measures with self-similar fractal support
- Creators
- Denise Szecsei
- Resource Type
- Journal article
- Publication Details
- Colloquium Mathematicum, Vol.109(2), pp.171-177
- DOI
- 10.4064/cm109-2-1
- ISSN
- 1730-6302
- eISSN
- 1730-6302
- Language
- English
- Date published
- 2007
- Academic Unit
- Computer Science; Mathematics
- Record Identifier
- 9983986086502771
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