Properties of Besov and Qp spaces in terms of the Schwarzian derivative of harmonic mappings

Key Points

• This paper aims to characterize log Jf's membership in Besov and Qp spaces through the Schwarzian derivative of harmonic mappings.
• Defined locally univalent, sense-preserving harmonic mappings in the unit disk.
• Characterized log Jf belonging to tilde{B}_p and tilde{Q}_p spaces using the Schwarzian derivative and Carleson measure.
• Introduced new classes BT_p and QT_p based on the Jacobian operator.
• Established criteria for log Jf to reside in Besov and Qp spaces using the Schwarzian derivative.
• Introduced new measurement classes, BT_p and QT_p, expanding the analysis of harmonic mappings.