A characterization of Lorentz-improving measures

Raymond J. Grinnell

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 ≤ 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:

PDF

Referencias


C. Graham, K. Hare, D. Ritter, The size of LP-improving measures, J. Funct. Anal. 84, 472-495 (1980).

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

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

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

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

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

Y. Sagher, On analytic famibes of operators, Israel, J. Math. 7, 350-:356 (1969).




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

Enlaces refback

  • No hay ningún enlace refback.