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Properties of the $\mathcal{M}$-Harmonic Conjugate Operator
Published online by Cambridge University Press: 20 November 2018
Abstract
We define the $\mathcal{M}$-harmonic conjugate operator $K$ and prove that it is bounded on the non-isotropic Lipschitz space and on $\text{BMO}$. Then we show $K$ maps Dini functions into the space of continuous functions on the unit sphere. We also prove the boundedness and compactness properties of $\mathcal{M}$-harmonic conjugate operator with ${{L}^{p}}$ symbol.
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- Research Article
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- Copyright © Canadian Mathematical Society 2003
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