Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 251-263

MARTINGALES AND SHARP BOUNDS FOR FOURIER MULTIPLIERS

Rodrigo Bañuelos and Adam Osekowski

Purdue University, Department of Mathematics
West Lafayette, IN 47907, U.S.A.; banuelos 'at' math.purdue.edu

University of Warsaw, Department of Mathematics, Informatics and Mechanics
Banacha 2, 02-097 Warsaw, Poland; ados 'at' mimuw.edu.pl

Abstract. Using the argument of Geiss, Montgomery-Smith and Saksman [14], and a new martingale inequality, the L^p-norms of certain Fourier multipliers in R^d, d \ge 2, are identified. These include, among others, the second order Riesz transforms R_j², j = 1,2,...,d, and some of the Lévy multipliers studied in [2], [3].

2010 Mathematics Subject Classification: Primary 42B15; Secondary 60G46.

Key words: Fourier multiplier, Riesz transform, martingale transform, differential subordination.

Reference to this article: R. Bañuelos and A. Osekowski: Martingales and sharp bounds for Fourier multipliers. Ann. Acad. Sci. Fenn. Math. 37 (2012), 251-263.

Full document as PDF file

doi:10.5186/aasfm.2012.3710

Copyright © 2012 by Academia Scientiarum Fennica