Extension of the Hardy-Littlewood-Fefferman-Stein inequality

Akihito Uchiyama

Vol. 120 (1985), No. 1, 229–255

DOI: 10.2140/pjm.1985.120.229

Abstract

We will show inequalities concerning the functions of the form f ∗ t⁻ⁿφ(⋅∕t)(x) defined on R₊ⁿ⁺¹ and give their applications to real Hardy spaces. These inequalities can be regarded as weak extensions of the Hardy-Littlewood-Fefferman-Stein inequality concerning harmonic functions.

Mathematical Subject Classification 2000

Primary: 42B25

Secondary: 42B30, 46E99

Milestones

Received: 4 January 1984

Published: 1 November 1985