Year: 2010
Type: preprint
Abstract: Let M denote the dyadic Maximal Function. We show that there is a weight w, and Haar multiplier T for which the following weak-type inequality fails: $$ \sup_{t>0}t w\left\{x\in\mathbb R \mid |Tf(x)|>t\right\}\le C \int_{\mathbb R}|f|Mw(x)dx. $$ (With T replaced by M, this is a well-known fact.) This shows that a dyadic version of the so-called Muckenhoupt-Wheeden Conjecture is false. This accomplished by using current techniques in weighted inequalities to show that a particular $L^2$ consequence of the inequality above does not hold.
Source: arXiv (Cornell University)
Author: Reguera, Maria Carmen
Institution: Georgia Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2953150733