Lusin area functions on local fields

Jia-Arng Chao

Vol. 59 (1975), No. 2, 383–390

DOI: 10.2140/pjm.1975.59.383

Abstract

We show that over a local field, Lusin area functions and nontangential maximal functions of a regular function are equivalent in the L^p “norm” for 0 < p < ∞. As a consequence, we have that “nice” singular integral transforms preserve H^p-spaces for 0 < p < ∞.

Mathematical Subject Classification 2000

Primary: 43A75

Milestones

Received: 20 February 1975

Published: 1 August 1975