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

• Autorzy: Kathryn E. Hare , Maria Roginskaya
• Języki publikacji: 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.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 43A05: Measures on groups and semigroups, etc.
• 28A12: Contents, measures, outer measures, capacities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 1
• Strony: 73-86

Daty

wydano

2005

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 Canada

autor

Maria Roginskaya

• Department of Mathematics, Chalmers TH and Göteborg University, Eklandagatan 86, Göteborg, SE 412 96 Sweden

Identyfikatory

DOI

10.4064/cm102-1-7