Disjointly homogeneous rearrangement invariant spaces via interpolation

作者：Astashkin S V^*

来源：Journal of Mathematical Analysis and Applications, 2015, 421(1): 338-361.

DOI：10.1016/j.jmaa.2014.07.020

• Rearrangement invariant space
• Lorentz space
• Marcinkiewicz space
• Orlicz space
• Real method of interpolation
• Calderon-Lozanovskii space

A Banach lattice E is called p-disjointly homogeneous, 1 <= p <= infinity, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l(p). Employing methods from interpolation theory, we clarify which r.i. spaces on [0,1] are p-disjointly homogeneous. In particular, for every 1 < p < infinity and any increasing concave function so on [0,1], which is not equivalent to neither 1 nor t(1), there exists a p-disjointly homogeneous r.i. space with the fundamental function phi. Moreover, it is shown that given 1 < p < infinity and an increasing concave p with non-trivial dilation indices, there is a unique p-disjointly homogeneous space among all interpolation spaces between the Lorentz and Marcinkiewicz spaces associated with phi.

• 出版日期2015-1-1