A dyadic analysis approach to the problem of continuity of weighted\n estimates with respect to the A_p characteristic

2015/02/02 by Nikolaos Pattakos, Pattakos, Nikolaos
Computer Science · Engineering · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1502.00435

openalex publication_date 2015/02/02 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

This paper presents a new proof of the results regarding the continuity of\nweighted estimates with respect to the characteristic of the weight. Here we\nfirst prove the result in the dyadic case which is "easier" and then by the use\nof the Bellman function technique we pass to the continuous setting which is\nharder in general. To be more precise, as far as we know, this passage from the\nMartingale transform to the Hilbert transform described in this note is new.\n

Citations

• Matrix weights, Littlewood Paley inequalities and the Riesz transforms
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular

Related

• A sharp estimate of weighted dyadic shifts of complexity 0 and 1
• On two weight estimates for dyadic operators
• On the failure of lower square function estimates in the non-homogeneous weighted setting
• Estimates for Bellman functions related to dyadic-like maximal operators\n on weighted spaces
• Martingale transforms, the dyadic shift and the Hilbert transform: a sufficient condition for boundedness between matrix weighted spaces