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Properties of the ℳ-Harmonic Conjugate Operator

Properties of the ℳ-Harmonic Conjugate Operator

Abstract We define the 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 ℳ-harmonic conjugate …