A characterization of Lorentz-improving measures

Raymond J. Grinnell


Let G be an infinite compact abelian group and let Ꞅ denote its dual group. A borel measure µ on G is called Lorentz-improving if there existe p, q1, and q2, where 1 < p < ꝏ and 1 ≤ q1q2 ≤ ꝏ, such that µ * L (p, q2) ⊆  L (p, q1). A detailed exposition of our recent characterization of Lorentz-improving measures is presented here. In this result Lorentz-improving measures are characterized in terms of the size of the sets {ϒ ∊ Ꞅ : │ µ (ϒ) │  > ∊ } and in terms of n-fold convolution powers. This characterization is analogous to a known characterization of LP-improving measures due to Hare.

Palabras clave

Measures on groups and semigroups; Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups; Spaces and other function spaces on groups

Texto completo:



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DOI: http://dx.doi.org/10.22199/S07160917.1995.0001.00004

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