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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak $ (1,1)$ boundedness of singular integrals with nonsmooth kernel


Author: Steve Hofmann
Journal: Proc. Amer. Math. Soc. 103 (1988), 260-264
MSC: Primary 42B20; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9939-1988-0938680-9
MathSciNet review: 938680
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Abstract: If $ \Omega \in {L^q}\left( {{S^1}} \right)$ for some $ q > 1,\int_{{S^1}} {\Omega = 0} $, and $ \Omega $ is homogeneous of degree 0, then the operator defined in two dimensions by $ {T_\varepsilon }f\left( x \right) = \int_{\left\vert y \right\vert > \varepsil... ...( {x - y} \right)\Omega \left( y \right){{\left\vert y \right\vert}^{ - 2}}dy} $ is of weak-type $ (1,1)$ with bound independent of $ \varepsilon > 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0938680-9
Article copyright: © Copyright 1988 American Mathematical Society