Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on Lp(G), 1 ≤ p < ∞, as was done by Helson. We will show how to ...

Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska-Orlicz indices of the ...

This paper studies properties of weakly analytic vector-valued measures, an area of study which is relatively unexplored, especially in comparison with scalar-valued measures.

This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of ...

The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear k-correlations of n > k independent random variables.

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the ...

Let X, Y and Z be Banach spaces, and let Πp(Y,Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T:X⊗εY→Z is 1-summing if and only if a ...

We show that the canonical embedding C(K) to LΦ(μ) has Gaussian cotype p, where μ is a Radon probability measure on K, and Φ is an Orlicz function equivalent to tp(log t)p/2 for large t.

We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz ...