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BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.

Joan Mateu, Joan Verdera Melenchón (1988)

Revista Matemática Iberoamericana

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...

Boundedness and compactness of some operators on discrete Morrey spaces

Martha Guzmán-Partida (2021)

Commentationes Mathematicae Universitatis Carolinae

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.

Boundedness for a bilinear model sum operator on ℝⁿ

Erin Terwilleger (2007)

Studia Mathematica

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.

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