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# Properties of the $\mathcal{M}$-Harmonic Conjugate Operator

Published:2003-03-01
Printed: Mar 2003
• Jaesung Lee
• Kyung Soo Rim
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## Abstract

We define the $\mathcal{M}$-harmonic conjugate operator $K$ and prove that it is bounded on the nonisotropic Lipschitz space and on $\BMO$. 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.
 Keywords: $\mathcal{M}$-harmonic conjugate operator $\mathcal{M}$-harmonic conjugate operator
 MSC Classifications: 32A70 - Functional analysis techniques [See mainly 46Exx] 47G10 - Integral operators [See also 45P05]

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