2025/04/05 by Zhirayr Avetisyan, Avetisyan, Zhirayr, Alexey Karapetyants +3
Mathematics · #44A05 #44A15 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2504.04127
openalex publication_date 2025/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of general homogeneous operators. This is the unique two-dimensional operator that has an antisymmetric kernel homogeneous with respect to all orientation-preserving linear transformations of the plane. It is shown that the operator under consideration interacts naturally, both in Cartesian and polar coordinates, with projective tensor products of some classical functional spaces, such as Lebesgue, Hardy, and Hölder spaces; conditions for their boundedness as operators acting from these spaces to Banach lattices of measurable functions and estimates of their norms are given.