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Hörmander's condition and a convolution operator generalizing Riesz potentials

Author: Jong-Guk Bak
Journal: Proc. Amer. Math. Soc. 120 (1994), 647-649
MSC: Primary 42B20; Secondary 47B35
MathSciNet review: 1195475
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Abstract: Under certain hypotheses including a Hörmander-type condition on the convolution kernel $ K$ we show that $ K{\ast}f$ belongs to the space $ \operatorname{BMO} ({{\mathbf{R}}^n})$ whenever $ f$ belongs to the space $ {L^{p,\infty }}({{\mathbf{R}}^n})$ (weak $ {L^p}$) for certain $ p$.

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