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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('cloak7ba093f7fb867962b7fa965c54bf7daa').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy7ba093f7fb867962b7fa965c54bf7daa = 'p&#105;c&#111;n' + '&#64;'; addy7ba093f7fb867962b7fa965c54bf7daa = addy7ba093f7fb867962b7fa965c54bf7daa + 'ffclrp' + '&#46;' + '&#117;sp' + '&#46;' + 'br'; var addy_text7ba093f7fb867962b7fa965c54bf7daa = 'p&#105;c&#111;n' + '&#64;' + 'ffclrp' + '&#46;' + '&#117;sp' + '&#46;' + 'br';document.getElementById('cloak7ba093f7fb867962b7fa965c54bf7daa').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy7ba093f7fb867962b7fa965c54bf7daa + '\'>'+addy_text7ba093f7fb867962b7fa965c54bf7daa+'<\/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).