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Strict $K$-monotonicity and $K$-order continuity in symmetric spaces. (arXiv:1705.06062v1 [math.FA])
来源于:arXiv
This paper is devoted to strict $K$- monotonicity and $K$-order continuity in
symmetric spaces. Using the local approach to the geometric structure in a
symmetric space $E$ we investigate a connection between strict $K$-monotonicity
and global convergence in measure of a sequence of the maximal functions. Next,
we solve an essential problem whether an existence of a point of $K$-order
continuity in a symmetric space $E$ on $[0,\infty)$ implies that the embedding
$E\hookrightarrow{L^1}[0,\infty)$ does not hold. We finish this article with a
complete characterization of $K$-order continuity in a symmetric space $E$ that
is written using a notion of order continuity under some assumptions on the
fundamental function of $E$. 查看全文>>