On a weak type (1,1) inequality for a maximal conjugate function

Nakhlé H. Asmar; Stephen J. Montgomery-Smith

ArticleOriginal scientific text

Title

On a weak type (1,1) inequality for a maximal conjugate function

Authors ¹, ¹

Affiliations

Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211 U.S.A.

Abstract

In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of

H^{p}

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.

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Title

On a weak type (1,1) inequality for a maximal conjugate function

Affiliations

Abstract

Bibliography