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Inclusion mappings between lp spaces

✍ Scribed by G Bennett


Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
324 KB
Volume
13
Category
Article
ISSN
0022-1236

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It is shown that if l . is an Orlicz sequence space, then the space l w 1 (l . ) of weakly summable sequences in l . is continuously embedded into l . (l 2 ) (resp., into l . (l . )) whenever t [ .(-t) is equivalent to a concave function (resp., a convex function and . is a supermultiplicative funct

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Let (Q, a, p) be a positive measure space and D ( p ) , 0 < p 5 00, the space of (equivalence classes of) functions which are p-integrable with respect to p. In a nice short paper [9] A. VILLANI stated necessary and sufficient conditions for the measure p such that inclusions of the form D ( p ) D (