Tohoku Mathematical Journal
2004
September
SECOND SERIES VOL. 56, NO. 3

Tohoku Math. J.
56 (2004), 371-392

Title UNIFORM TWO-WEIGHT NORM INEQUALITIES FOR HANKEL TRANSFORM BOCHNER-RIESZ MEANS OF ORDER ONE

Author Óscar Ciaurri, Krzysztof Stempak and Juan L. Varona

(Received December 18, 2002, revised November 14, 2003)
Abstract. Two-weight $L^p$ norm inequalities, uniform with respect to the order of the involved Bessel function, are proved for the Bochner-Riesz means of the first order for the Hankel transform. Both sufficient and necessary conditions for parameters used in the two weights are determined. The proof relies on uniform pointwise asymptotic estimates for the Bessel functions that were shown by Barceló and Córdoba.

2000 Mathematics Subject Classification. Primary 42C10; Secondary 44A20.
Key words and phrases. Bochner-Riesz means, Hankel transform, Bessel functions, two-weight norm inequalities.

To the top of this page

Back to the Contents