Hi everybody.
I need some information about the set of real functions L^1 \cap L^{\infty}.
Does anyone have some source, book, paper about it?
I need some properties like completeness (or closure), density, rel. compactness,..etc.
best regards.
Ricardo.
You can read
https://math.stackexchange.com/questions/662590/why-is-l1-cap-l-infty-dense-is-in-lp
and I have attached a file that I hope will help you
See, for example the book
S. G. Krein, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Amer. Math. Soc., Providence 1982.
See also the following paper
Astashkin, Sergey V.; Maligranda, Lech. $L_p+L_\infty$ and $L_p\cap L_\infty$ are not isomorphic for all $1\leq p
What about the interpolation bible? C. Bennett and R. Sharpley:
Interpolation of operators, Academic Press, 1988.
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