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

http://dx.doi.org/10.4153/CMB-2003-011-x
Canad. Math. Bull. 46(2003), 113-121

  Published:2003-03-01
 Printed: Mar 2003

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.