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

Published online by Cambridge University Press:  20 November 2018

Jaesung Lee  and
Kyung Soo Rim
Jaesung Lee
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea, e-mail: jalee@sogang.ac.kr
Kyung Soo Rim
Affiliation:
DIP Lab Corp., Bangwoo B/D 636-2, Shinsa Kangnam, Seoul 135-869, Korea, e-mail: ksrim@diplab.com
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Abstract

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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.

Keywords

32A7047G10$\mathcal{M}$-harmonic conjugate operator
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 113 - 121
Copyright
Copyright © Canadian Mathematical Society 2003

References

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