The Helicoidal Method

2018/01/30 by Cristina Benea, Benea, Cristina, Camil Muscalu +1 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #math.CA

paper · pdf · doi:10.48550/arxiv.1801.10071

expository paper, 47 pages

arxiv created 2018/05/17 · arxiv updated 2018/05/18

Abstract

This is an expository paper on the helicoidal method, a tool designed for proving multiple vector-valued inequalities for operators in harmonic analysis, which is based on stopping times and localizations. As it turns out, the local estimate can be used for proving sparse domination for the scalar operator and its multiple vector-valued extensions, and hence also weighted estimates.

Citations

• On commutators of singular integrals and bilinear singular integrals
• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory
• Some Maximal Inequalities

Cited by

• Generalized Carleson Embeddings into Weighted Outer Measure Spaces
• End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Related

• Sparse domination via the helicoidal method
• An introduction to pointwise sparse domination
• Quasi-Banach Valued Inequalities via the Helicoidal method
• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• Sparse domination via the Calderón-Zygmund decomposition: the example of Dini-smooth kernels