|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Certain Multi(sub)linear square functions | | Loukas Grafakos
; Sha He
; Qingying Xue
; | | Date: |
14 Apr 2015 | | Abstract: | Let $dge 1, ellin^d$, $min mathbb Z^+$ and $ heta_i$, $i=1,dots,m $
are fixed, distinct and nonzero real numbers. We show that the $m$-(sub)linear
version below of the Ratnakumar and Shrivastava cite{RS1} Littlewood-Paley
square function $$T(f_1,dots ,
f_m)(x)=Big(sumlimits_{ellin^d}|int_{mathbb{R}^d}f_1(x- heta_1
y)cdots f_m(x- heta_m y)e^{2pi i ell cdot y}K (y)dy|^2Big)^{1/2} $$ is
bounded from $L^{p_1}(mathbb{R}^d) imescdots imes L^{p_m}(mathbb{R}^d) $
to $L^p(mathbb{R}^d) $ when $2le p_i<infty$ satisfy $1/p=1/p_1+cdots+1/p_m$
and $1le p<infty$. Our proof is based on a modification of an inequality of
Guliyev and Nazirova cite{GN} concerning multilinear convolutions. | | Source: | arXiv, 1504.3424 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
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 Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER