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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, 47G10 show english descriptions Functional analysis techniques [See mainly 46Exx]
Integral operators [See also 45P05]
32A70 - Functional analysis techniques [See mainly 46Exx]
47G10 - Integral operators [See also 45P05]
 

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