A cancellative amenable ascending union of nonamenable semigroups
We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.
A Hilbert transform for non-homogeneous martingales
A note on analytic measures.
Approximation of Hp-functions by Bochner-Riesz means of compact Lie groups.
Compensated compactness and the Heisenberg group.
Compensated compactness and the Heisenberg group.
Conjugate Characterizations of H1 Dyadic Martingales.
Continuous rearrangements of the Haar system in for 0 < p < ∞
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
Decomposition of analytic measures on groups and measure spaces
We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, acting on a space of measures. Under suitable conditions, we define the notion of analytic measures using the representation of G and the order on Γ. Our goal is to study analytic measures by applying a new transference principle for subspaces of measures, along with results from probability and Littlewood-Paley theory. As a consequence, we derive new properties of analytic measures as well as extensions of previous...
Dirichlet series induced by the Riemann zeta-function
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.
Extension of multiplicative families of isometries. (Extensión de familias multiplicativas de isometrías.)
Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program
For the scalar holomorphic discrete series representations of and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside . We construct a Cayley transform between the Ol’shanskiĭ semigroup having as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for . This allows calculating the composition series in terms of harmonic analysis on . In particular we show that the Ol’shanskiĭ Hardy space for is different...
Generalized conjugate systems on local fields
Hahn's Embedding Theorem for orders and harmonic analysis on groups with ordered duals
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 , 1 ≤ p < ∞, as was done by Helson [7]. We will show how to use Hahn’s Embedding Theorem for orders and the ergodic Hilbert transform to study the conjugate function. Our approach enables us to define a filtration of the Borel σ-algebra on G, which in turn will allow us to introduce tools from martingale theory into the analysis on groups...
Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space
On a weak type (1,1) inequality for a maximal conjugate function
In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.
On vector-valued Hardy martingales and a generalized Jensen's inequality.
The conjugation operator on .
The F. and M. Riesz theorem revisited.
The Rockland condition for nondifferential convolution operators II