A characterization of Lorentz-improving measures

  • Raymond J. Grinnell University of the West Indies Bridgetown.
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

Resumen

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 ≤ q1 ≤ q2 ≤ 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.

Biografía del autor/a

Raymond J. Grinnell, University of the West Indies Bridgetown.
Department of Mathématic: and Computer Science.

Citas

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[2] R. Grinnell, K. Hare, Lorentz-improving measures, Ill. J. Math. 38 No. 3, 366-389 (1994).

[3] R. Grinnell, Lorentz-improving mesures on compact abelian groups, Ph.D. dissertation, Queen's University (1991).

[4] K. Hare, A characterization of LP -improving measures, Proc. Amer.; Math. Soc. 102, 295-299 (1988).

[5] E. Hewitt, K. Ross, Abstract harmonic analysis, Vol. II, Springer-Verlag, New York (1970).

[6] Y. Katznelson, An introduction to harmonic analysis, Dover, New York (1976).

[7] Y. Sagher, On analytic famibes of operators, Israel, J. Math. 7, 350-:356 (1969).
Publicado
2018-04-03
Cómo citar
Grinnell, R. (2018). A characterization of Lorentz-improving measures. Proyecciones. Journal of Mathematics, 14(1), 43-50. https://doi.org/10.22199/S07160917.1995.0001.00004
Sección
Artículos