Vol. 21, No. 3, 1967

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A note of dilations in Lp

Sav Roman Harasymiv

Vol. 21 (1967), No. 3, 493–501
Abstract

The objects of study in this note are the Lebesgue spaces Lp(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

f(a1x1 + b1,⋅⋅⋅ ,anxn + bn)

where a1,,an,b1,,bn R, and a10,,an0.

Mathematical Subject Classification
Primary: 42.18
Milestones
Received: 20 July 1965
Published: 1 June 1967
Authors
Sav Roman Harasymiv