Bounds on the Walsh model for $M^{q,*}$ Carleson and related operators

Richard Oberlin

doi:10.4171/rmi/742

JournalsrmiVol. 29, No. 3pp. 829–857

Bounds on the Walsh model for $M^{q, *}$ Carleson and related operators

Richard Oberlin
Louisiana State University, Baton Rouge, USA

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Abstract

We prove an extension of the Walsh-analog of the Carleson–Hunt theorem, where the $L^{\infty}$ norm defining the Carleson maximal operator has been replaced by an $L^{q}$ maximal-multiplier-norm. Additionally, we consider certain associated variation-norm estimates.

Cite this article

Richard Oberlin, Bounds on the Walsh model for $M^{q, *}$ Carleson and related operators. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 829–857

DOI 10.4171/RMI/742