A note of dilations in L^p

Sav Roman Harasymiv

Vol. 21 (1967), No. 3, 493–501

DOI: 10.2140/pjm.1967.21.493

Abstract

The objects of study in this note are the Lebesgue spaces L^p(1 < p < ∞) on the n-dimensional Euclidean space Rⁿ. We consider a function f one of the above-mentioned spaces, and derive results about the closure (in the relevant function space) of the set of linear combinations of functions of the form

where a₁,⋯,a_n,b₁,⋯,b_n ∈ R, and a₁≠0,⋯,a_n≠0.

Mathematical Subject Classification

Primary: 42.18

Milestones

Received: 20 July 1965

Published: 1 June 1967