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...

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space H Cn of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap...

Abstract We develop a theory of pointwise wedge products vector-valued functions on the circle and disc, obtain results which give rise to new approach analysis matricial Nehari problem. investigate properties creation operators orthogonal complements in context operator study analytic unit disc.

a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...

In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The can generate approximate samples from posteriors efficiently. Based on concepts operator-valued kernels and vector-valued reproducing kernel Hilbert spaces, a rigorous definition is given objects, e.g., operator, which are proved to be lim...

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...