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• # Artykuł - szczegóły

## Colloquium Mathematicum

2005 | 102 | 1 | 73-86

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

EN

### Abstrakty

EN
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.

73-86

wydano
2005

### Twórcy

autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 Canada
autor
• Department of Mathematics, Chalmers TH and Göteborg University, Eklandagatan 86, Göteborg, SE 412 96 Sweden