Logarithmic L^p bounds for maximal directional singular integrals in the\n plane

2012/03/29 by Ciprian Demeter, Demeter, Ciprian, Francesco Di Plinio +1
Computer Science · Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1203.6624

openalex publication_date 2012/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the L^p-boundedness of maximal singular integrals in the plane\nover a finite set V of N directions. Logarithmic bounds are established for a\nset V of arbitrary structure in the 2<=p<infinity range. Sharp bounds are\nproved for lacunary and Vargas sets of directions. The latter include the case\nof uniformly distributed directions and the finite truncations of the Cantor\nset.\n We make use of both classical harmonic analysis methods and product-BMO based\ntime-frequency analysis techniques. As a further application of the latter, we\nderive an L^p almost orthogonality principle for Fourier restrictions to cones.\n

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