6 papers · 1 filter
Decomposition of analytic measures on groups and measure spaces
Nakhle Asmar, Stephen Montgomery-Smith
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 an…
Transference in spaces of measures
Nakhlé Asmar, Stephen J. Montgomery-Smith, Sadahiro Saeki
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operat…
Hardy martingales and Jensen's Inequality
N. Asmar, Stephen J. Montgomery-Smith
We extend ideas of Garling to consider the so called Hardy martingales in a more general setting of H^p theory of compact abelian groups with ordered dual. As a consequence, we obt…
A Note on UMD Spaces and Transference in Vector-valued Function Spaces
N. Asmar, B. Kelly, Stephen J. Montgomery-Smith
We introduce the notion of an ACF space, that is, a space for which a generalized version of M. Riesz's theorem for conjugate functions with values in the Banach space is bounded.…
On a weak type (1,1) inequality for a maximal conjugate function
N. Asmar, Stephen J. Montgomery-Smith
In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of H^p spaces for 0 < p < infinity. In this paper, we s…
On the distribution of Sidon series
Nakhlé Asmar, Stephen J. Montgomery-Smith
Let B denote an arbitrary Banach space, G a compact abelian group with Haar measure and dual group . Let E be a Sidon subset of with Sidon constant S(E). Let r_n denote…