Carlson type inequalities and embeddings of interpolation spaces

Larsson, Leo

doi:10.1090/S0002-9939-04-07357-5

Carlson type inequalities and embeddings of interpolation spaces
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Proc. Amer. Math. Soc. 132 (2004), 2351-2356 Request permission

Abstract:

We discuss the close relation between Carlson type inequalities \[ \|a\|_X\leq K\|a\|_{A_0}^{1-\theta }\|a\|_{A_1}^\theta \] and interpolation, and prove embedding results for real interpolation spaces, in particular into weighted $L_p$-spaces.

References

Sorina Barza, Victor Burenkov, Josip Pe arić, and Lars-Erik Persson, Sharp multidimensional multiplicative inequalities for weighted $L_p$ spaces with homogeneous weights, Math. Inequal. Appl. 1 (1998), no. 1, 53–67. MR 1492910, DOI 10.7153/mia-01-04
Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275, DOI 10.1007/978-3-642-66451-9
Carlson, F.: Une inégalité, Ark. Mat. Astr. Fysik 25B (1934), No. 1.
Jan Gustavsson and Jaak Peetre, Interpolation of Orlicz spaces, Studia Math. 60 (1977), no. 1, 33–59. MR 438102, DOI 10.4064/sm-60-1-33-59
Natan Ya. Kruglyak, Lech Maligranda, and Lars Erik Persson, A Carlson type inequality with blocks and interpolation, Studia Math. 104 (1993), no. 2, 161–180. MR 1211816, DOI 10.4064/sm-104-2-161-180
Leo Larsson, A new Carlson type inequality, Math. Inequal. Appl. 6 (2003), no. 1, 55–79. MR 1950651, DOI 10.7153/mia-06-06
Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
Lech Maligranda and Lars E. Persson, Real interpolation between weighted $L^p$ and Lorentz spaces, Bull. Polish Acad. Sci. Math. 35 (1987), no. 11-12, 765–778 (English, with Russian summary). MR 961715