A NEW CLASS OF RESTRICTED TYPE SPACES

作者：Rodriguez Lopez Salvador^*; Soria Javier

来源：Proceedings of the Edinburgh Mathematical Society, 2011, 54: 749-759.

DOI：10.1017/S0013091509001710

• rearrangement-invariant spaces
• restricted type
• Lorentz spaces

We find new properties for the space R(X), introduced by Soria in the study of the best constant for the Hardy operator minus the identity. In particular, we characterize when R(X) coincides with the minimal Lorentz space Lambda(X). The condition that R(X) not equal {0} is also described in terms of the embedding (L-1,L-infinity boolean AND L-infinity) subset of X. Finally, we also show the existence of a minimal rearrangement-invariant Banach function space (RIBFS) X among those for which R(X) not equal {0} (which is the RIBFS envelope of the quasi-Banach space L-1,L-infinity boolean AND L-infinity).

• 出版日期2011-10