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When Is Lr(R) Contained in Lp(R) + Lq(R)?

Jean-Baptiste Hiriart-Urruty and Patrice Lassère
The American Mathematical Monthly
Vol. 120, No. 1 (January 2013), pp. 55-61
DOI: 10.4169/amer.math.monthly.120.01.055
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Page Count: 7
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When Is Lr(R) Contained in Lp(R) + Lq(R)?
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Abstract We prove a necessary and sufficient condition on the exponents p, q, r ≥ 1 such that Lr (R) ⊂ Lp(R) + Lq(R). In doing so, we explore the structure of Lp(R) + Lq(R) as a normed vector space.

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