Biorthogonalité et théorie des opérateurs.
The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on , , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.
The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...
MSC 2010: 42B10, 44A15In this paper we prove Bochner-Hecke theorems for the Weinstein transform and we give an application to homogeneous distributions.
We consider discrete versions of Morrey spaces introduced by Gunawan et al. in papers published in 2018 and 2019. We prove continuity and compactness of multiplication operators and commutators acting on them.
We study a multilinear oscillatory integral with rough kernel and establish a boundedness criterion.
The purpose of this article is to obtain a multidimensional extension of Lacey and Thiele's result on the boundedness of a model sum which plays a crucial role in the boundedness of the bilinear Hilbert transform in one dimension. This proof is a simplification of the original proof of Lacey and Thiele modeled after the presentation of Bilyk and Grafakos.