Abstract
In this paper, we define the \(L^\varphi \)-Lipschitz norm and \(L^\varphi \)-BMO norm of differential forms using Young functions, and prove the comparison theorems for the homotopy operator T on differential forms with \(L^\varphi \)-Lipschitz and \(L^\varphi \)-BMO norms. As applications, we give the \(L^\varphi \)-BMO norm estimate for conjugate A-harmonic tensors and the weighted \(L^\varphi \)-Lipschitz norm estimate for the homotopy operator T.
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All authors put their efforts together on the research and writing of this manuscript. Xuexin Li carried out the proofs of all research results in this manuscript, and wrote its draft. Yuming Xing and Jinling Niu proposed the study, participated in its design and revised its final version. All authors read and approved the final manuscript.
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Li, X., Niu, J. & Xing, Y. Estimates for \(L^\varphi \)-Lipschitz and \(L^\varphi \)-BMO Norms of Differential Forms. Complex Anal. Oper. Theory 13, 1811–1825 (2019). https://doi.org/10.1007/s11785-018-0859-5
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DOI: https://doi.org/10.1007/s11785-018-0859-5