Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'488'730
Articles rated: 2609

29 March 2024
 
  » arxiv » 1711.7084

 Article overview


Superexponential estimates and weighted lower bounds for the square function
Paata Ivanisvili ; Sergei Treil ;
Date 19 Nov 2017
AbstractWe prove the following superexponential distribution inequality: for any integrable $g$ on $[0,1)^{d}$ with zero average, and any $lambda>0$ [ |{ x in [0,1)^{d} ; :; g geqlambda }| leq e^{- lambda^{2}/(2^{d}|S(g)|_{infty}^{2})}, ] where $S(g)$ denotes the classical dyadic square function in $[0,1)^{d}$. The estimate is sharp when dimension $d$ tends to infinity in the sense that the constant $2^{d}$ in the denominator cannot be replaced by $C2^{d}$ with $0<C<1$ independent of $d$ when $d o infty$.
For $d=1$ this is a classical result of Chang--Wilson--Wolff [4]; however, in the case $d>1$ they work with a special square function $S_infty$, and their result does not imply the estimates for the classical square function.
Using good $lambda$ inequalities technique we then obtain unweighted and weighted $L^p$ lower bounds for $S$; to get the corresponding good $lambda$ inequalities we need to modify the classical construction.
We also show how to obtain our superexponential distribution inequality (although with worse constants) from the weighted $L^2$ lower bounds for $S$, obtained in [5].
Source arXiv, 1711.7084
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica