## View abstract

### Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Tuesday, July 20, 17:10 ~ 17:40 UTC-3

## Stein-Weiss inequality in $L^{1}$ norm for vector fields

### Tiago Picon

#### University of São Paulo, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakcacf988ed921f3b56d11d706a3d8190b').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addycacf988ed921f3b56d11d706a3d8190b = 'p&#105;c&#111;n' + '&#64;'; addycacf988ed921f3b56d11d706a3d8190b = addycacf988ed921f3b56d11d706a3d8190b + 'ffclrp' + '&#46;' + '&#117;sp' + '&#46;' + 'br'; var addy_textcacf988ed921f3b56d11d706a3d8190b = 'p&#105;c&#111;n' + '&#64;' + 'ffclrp' + '&#46;' + '&#117;sp' + '&#46;' + 'br';document.getElementById('cloakcacf988ed921f3b56d11d706a3d8190b').innerHTML += '<a ' + path + '\'' + prefix + ':' + addycacf988ed921f3b56d11d706a3d8190b + '\'>'+addy_textcacf988ed921f3b56d11d706a3d8190b+'<\/a>';

In this talk, we investigate the limit case $p=1$ of the Stein-Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators. As application, we recovered some classical div-curl inequalities in literature. In addition, we also discussed a two-weight inequality with general weights extending the previous result due to Sawyer for the scalar case.

Joint work with Pablo De Nápoli (Universidad de Buenos Aires , Argentina).