We give a full solution of the following problems concerning the spaces : (i) to what extent two functions φ and ψ should be different in order to ensure that for any nontrivial Banach couple X⃗; (ii) when an embedding can (or cannot) be dense; (iii) which Banach space can be regarded as an -space for some (unknown beforehand) Banach couple X⃗.
We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t (ln (e/t) with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L.
We consider quasilinear operators T of
Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {a*} mean the decreasing rearrangement of a sequence {|a|}. A sequence space l with symmetric (quasi)norm || {φ(n)a*} || is called , because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λ and M. We study properties of the spaces l for all admissible parameters φ, E and use them...
Page 1