Some inclusion theorems for sequence spaces

Grahame Bennett

Vol. 46 (1973), No. 1, 17–30

DOI: 10.2140/pjm.1973.46.17

Abstract

The purpose of this paper is to study inclusion theorems for some of the more familiar sequence spaces. Necessary and sufficient conditions are given for an FK-space to contain each of the spaces bv₀, bv, l^p,0 < p < ∞, and c₀. It is also shown that the Hardy space H^p,0 < p < 1, is a barrelled subspace of its containing Banach space B^p. This leads to new results concerning multipliers of H^p and to new estimates on the growth of the Taylor coefficients of B^p functions.

Mathematical Subject Classification 2000

Primary: 46A45

Milestones

Received: 4 February 1972

Published: 1 May 1973