标题： K-单调加权巴拿赫对的新例子 显示英文标题

标题： New examples of K-monotone weighted Banach couples

摘要： 一些新的K-单调对的例子，形式为(X, X(w))，其中X是[0, 1]上的对称空间，w是[0, 1]上的权函数，被提出。 基于对称空间的w可分解性性质，我们证明了，如果权函数w变化足够快，所有具有非平凡Boyd指数的对称空间X，使得Banach对(X, X(w))是K-单调的，都属于超对称Orlicz空间类。 如果X的基本函数是t^{1/p}，对于某个p \in [1, \infty ]，则X = L_p。 同时，在X不是超对称的情况下，对于某些非平凡的w，Banach对(X, X(w))也可能是K-单调的。 在X是Lorentz空间、Marcinkiewicz空间或Orlicz空间的每种情况下，我们都找到了保证(X, X(w))是K-单调的条件。 显示英文摘要

摘要： Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X, X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t^{1/p} for some p \in [1, \infty], then X = L_p. At the same time a Banach couple (X, X(w)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space we have found conditions which guarantee that (X, X(w)) is K-monotone.