Intersection of Lebesgue spaces 𝐿₁ and 𝐿₂

Intersection of Lebesgue spaces $L_ 1$ and $L_ 2$
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Proc. Amer. Math. Soc. 103 (1988), 1185-1188

DOI: https://doi.org/10.1090/S0002-9939-1988-0955005-3

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The linear topological properties of the intersection of Lebesgue spaces ${L_1}$ and ${L_2}$ are investigated.

References

D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 270–286. MR 730072
N. L. Carothers and S. J. Dilworth, Geometry of Lorentz spaces via interpolation, Texas Functional Analysis Seminar 1985–1986 (Austin, TX, 1985–1986) Longhorn Notes, Univ. Texas, Austin, TX, 1986, pp. 107–133. MR 1017049

Equidistributed random variables in

Subspaces of

N. L. Carothers and S. J. Dilworth, Inequalities for sums of independent random variables, Proc. Amer. Math. Soc. 104 (1988), no. 1, 221–226. MR 958071, DOI 10.1090/S0002-9939-1988-0958071-4
Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
S. J. Dilworth, Interpolation of intersections of $L_p$ spaces, Arch. Math. (Basel) 50 (1988), no. 1, 51–55. MR 925494, DOI 10.1007/BF01313494

Some linear topological properties of the Hardy spaces

33

J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249. MR 0291772, DOI 10.1016/0022-1236(71)90011-5
Bernard Maurey, Isomorphismes entre espaces $H_{1}$, Acta Math. 145 (1980), no. 1-2, 79–120 (French). MR 586594, DOI 10.1007/BF02414186
A. Pełczyński, On the impossibility of embedding of the space $L$ in certain Banach spaces, Colloq. Math. 8 (1961), 199–203. MR 131154, DOI 10.4064/cm-8-2-199-203
Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972