On the dimensional weak-type (1,1) bound for Riesz transforms

DOI10.1142/S0219199720500728zbMath1476.42013arXiv2004.03382OpenAlexW3107429280MaRDI QIDQ5159142

Daniel E. Spector, Cody B. Stockdale

Publication date: 26 October 2021

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.03382

zbMATH Keywords

Riesz transformsweak-type estimatesdimensional dependence

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06)

Cites Work

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• Lower bounds for the weak type \((1, 1)\) estimate for the maximal function associated to cubes in high dimensions
• On the existence of certain singular integrals
• The development of square functions in the work of A. Zygmund
• Some results in harmonic analysis in 𝐑ⁿ, for 𝐧→∞
• Weak-type estimates for singular integrals and the Riesz transform
• A limited-range Calder\'on-Zygmund theorem
• Classical Fourier Analysis
• A note on the Hilbert transform

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