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

Hugo Arbeláez; Rodrigo Hernández; Willy Sierra

doi:10.2298/FIL2535445A

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

Hugo Arbeláez
, Rodrigo Hernández
, Willy Sierra

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we give a characterization of log J_f belongs to^˜B_p or^˜Q_p spaces for any locally univalent sense-preserving harmonic mappings f defined in the unit disk, using the Schwarzian derivative of f and Carleson measure. In addition, we introduce the classes BT_p and QT_p, based on the Jacobian operator, and initiate a study of these spaces.

Original language	English
Pages (from-to)	12445-12459
Number of pages	15
Journal	Filomat
Volume	39
Issue number	35
DOIs	https://doi.org/10.2298/FIL2535445A
State	Published - 2025

Keywords

Besov space
Harmonic mapping
Q space
Schwarzian derivative

Access to Document

10.2298/FIL2535445A

Cite this

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title = "Properties of Besov and Qp spaces in terms of the Schwarzian derivative of harmonic mappings",

abstract = "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 measure. In addition, we introduce the classes BTp and QTp, based on the Jacobian operator, and initiate a study of these spaces.",

keywords = "Besov space, Harmonic mapping, Q space, Schwarzian derivative",

author = "Hugo Arbel{\'a}ez and Rodrigo Hern{\'a}ndez and Willy Sierra",

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AU - Arbeláez, Hugo

AU - Hernández, Rodrigo

AU - Sierra, Willy

PY - 2025

Y1 - 2025

N2 - 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 measure. In addition, we introduce the classes BTp and QTp, based on the Jacobian operator, and initiate a study of these spaces.

AB - 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 measure. In addition, we introduce the classes BTp and QTp, based on the Jacobian operator, and initiate a study of these spaces.

KW - Besov space

KW - Harmonic mapping

KW - Q space

KW - Schwarzian derivative

UR - https://www.scopus.com/pages/publications/105028490101

U2 - 10.2298/FIL2535445A

DO - 10.2298/FIL2535445A

M3 - Article

AN - SCOPUS:105028490101

SN - 0354-5180

VL - 39

SP - 12445

EP - 12459

JO - Filomat

JF - Filomat

IS - 35