Browsing Department of Mathematics (MU) by Author "Asmar, Nakhlé H."
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Analytic measures and Bochner measurability
MontgomerySmith, Stephen, 1963; Asmar, Nakhlé H. (201101)Many authors have made great strides in extending the celebrated F. and M. Riesz Theorem to various abstract settings. Most notably, we have, in chronological order, the work of Bochner, Helson and Lowdenslager, de Leeuw ... 
Decomposition of analytic measures on groups and measure spaces
MontgomerySmith, Stephen, 1963; Asmar, Nakhlé H. (201101)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 ... 
Hahn's embedding theorem for orders and harmonic analysis on groups with ordered duals
Asmar, Nakhlé H.; MontgomerySmith, Stephen, 1963 (201101)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 ... 
Hardy martingales and Jensen's inequality
MontgomerySmith, Stephen, 1963; Asmar, Nakhlé H. (201102)Hardy martingales were introduced by Garling and used to study analytic functions on the Ndimensional torus TN, where analyticity is defined using a lexicographic order on the dual group ZN. We show how, by using basic ... 
On a weak type (1, 1) inequality for a maximal conjugate function
Asmar, Nakhlé H.; MontgomerySmith, Stephen, 1963 (201101)In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions ... 
A transference theorem for ergodic H1
MontgomerySmith, Stephen, 1963; Asmar, Nakhlé H. (201101)In this paper, we extend the basic transference theorem for convolution operators on Lp spaces of Coifman and Weiss to H1 spaces. 
Vectorvalued weakly analytic measures
Asmar, Nakhlé H.; Kelly, Annela R.; MontgomerySmith, Stephen, 1963 (201101)This paper studies properties of weakly analytic vectorvalued measures, an area of study which is relatively unexplored, especially in comparison with scalarvalued measures.