𝐿^{∞}-BMO boundedness for a singular integral operator

Namazi, Javad

doi:10.1090/S0002-9939-1990-0998738-4

$L^ \infty$-BMO boundedness for a singular integral operator
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by Javad Namazi

Proc. Amer. Math. Soc. 108 (1990), 465-470

DOI: https://doi.org/10.1090/S0002-9939-1990-0998738-4

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Abstract:

If $K\left ( x \right ) = \Omega \left ( x \right )/|x{|^n}$ is a Calderón-Zygmund kernel and $b\left ( {|x|} \right )$ 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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