A Class of Multiparameter Oscillatory Singular Integral Operators: Endpoint Hardy Space Bounds

2018/03/02 by Bakas, Odysseas, Latorre, Eric, Martínez, Diana Cristina Rincón +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.01046

Abstract

We establish endpoint bounds on a Hardy space H¹ for a natural class of multiparameter singular integral operators which do not decay away from the support of rectangular atoms. Hence the usual argument via a Journé-type covering lemma to deduce bounds on product H¹ is not valid. We consider the class of multiparameter oscillatory singular integral operators given by convolution with the classical multiple Hilbert transform kernel modulated by a general polynomial oscillation. Various characterisations are known which give L² (or more generally L^p, 1

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