Radial multipliers and restriction to surfaces of the Fourier transform\n in mixed-norm spaces

2016/01/15 by Antonio Córdoba, Córdoba, Antonio, Latorre, Eric
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1601.03870

openalex publication_date 2016/01/15 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In this article we revisit some classical conjectures in harmonic analysis in\nthe setting of mixed norm spaces L^p_rad L²_ang (\ℝⁿ). We\nproduce sharp bounds for the restriction of the Fourier transform to compact\nhypersurfaces of revolution in the mixed norm setting and study an extension of\nthe disc multiplier. We also present some results for the discrete restriction\nconjecture and state an intriguing open problem.\n

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