We consider semi-group BMO spaces associated with an arbitrary $\sigma$-finite von Neumann algebra $(\mathcal{M}, \varphi)$. prove that the row and column always admit a predual, extending results from finite case. Consequently, we can considered are Banach they interpolate $L_p$ as in commutative situation, namely $[\mathrm{BMO}(\mathcal{M}), L_p^\circ(\mathcal{M})]_{1/q} \approx L_{pq}^\circ(...

The function spaces Dk(R) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp = n, obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div–curl, and related Hodge systems, C. R. Math. Acad. Sci. Paris 338 (7) (2004) 539–543 (see also J. Van Schaftingen, Estimates for L1-vector fields...

We characterize time-consistent dynamic risk measures. In discrete time in context of uncertainty, we canonically associate a class of probability measures to any dynamic risk measure when the filtration comes from a process bounded at each time. Dynamic risk measures are conditional risk measures on a bigger space. In continuous time, we characterize time consistency, studying composition of c...

H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H(⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H(⊗1 C+) given by Hbφ = Pbφ. We show that ‖Hb‖ ≃ ‖Pb‖BMO(⊗n 1 C+), where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well known e...

We prove that the multiparameter (product) space BMO of functions of bounded mean oscillation can be written as the intersection of finitely many dyadic product BMO spaces, with equivalent norms, generalizing the one-parameter result of T. Mei. We establish the analogous dyadic structure theorems for the space VMO of functions of vanishing mean oscillation, for Ap weights, for reverse-Hölder we...

Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...

Many combinatorial optimization problems entail a number of hierarchically dependent optimization problems. An often used solution is to associate a suitably large cost with each individual optimization problem, such that the solution of the resulting aggregated optimization problem solves the original set of optimization problems. This paper starts by studying the package upgradeability proble...