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In this paper we give a characterization of log Jf belongs to Bₚ or Qₚ spaces for any locally univalent sense-preserving harmonic mappings f defined in the unit disk, using the Schwarzian derivative of f and Carleson meseaure. In addition, we introduce the classes BTₚ and QTₚ, based on the Jacobian operator, and begin a study of these.
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Arbeláez et al. (2024) studied this question.
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