In this paper, we establish CBMO estimates for the multilinear commutator related to the Marcinkiewicz operator in Herz and Morrey-Herz spaces.

In this paper, the (H ~b , L p) and (HK̇ q,~b , K̇ q ) type boundedness for the multilinear commutator associated with the Littlewood-paley operator are obtained.

We logically model uncertainty by expanding language without changing logical reasoning rules. We expand the language of set theory by adding new predicate symbols, uncertain membership relations ∈+ and ∈−. We define the set theory ZF± as an extension of ZF with new symbols in classical logic. In this system we can represent uncertainty which is naturally represented in the model of 3-valued lo...

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes, which in the real valued case can be replaced by simpler norms of the kernel matrix (i.e. norms of some multilinear operators associated with the kernel matrix). As a corollary we derive tail inequalities for U-statisti...

This paper deals with the causality structure of multilinear, multipower operators on a Hilbert resolution space. One objective of this study is to clear up certain unanswered questions raised in [l]. In particular we present a counterexample consisting of a compact set K C&(0, 1) such that no memoryless multipower operators of order n >, 2 can be defined on K. This lays to rest the tempting co...