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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ L\sp \infty$-BMO boundedness for a singular integral operator


Author: Javad Namazi
Journal: Proc. Amer. Math. Soc. 108 (1990), 465-470
MSC: Primary 42B20; Secondary 47G05
MathSciNet review: 998738
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Abstract: If $ K\left( x \right) = \Omega \left( x \right)/\vert x{\vert^n}$ is a Calderón-Zygmund kernel and $ b\left( {\vert x\vert} \right)$ is a bounded radial function, we find conditions on $ b$ such that the singular operator whose kernel is $ b\left( x \right)K\left( x \right)$ is bounded from $ {L^\infty }\left( {{R^n}} \right)$ to $ {\text{BMO}}\left( {{R^n}} \right)$, or equivalently from $ {H^1}\left( {{R^n}} \right)$ into $ {L^1}\left( {{R^n}} \right)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0998738-4
PII: S 0002-9939(1990)0998738-4
Keywords: Calderón-Zygmund kernels
Article copyright: © Copyright 1990 American Mathematical Society