Restrictions of B\'ekoll\'e--Bonami weights and Bloch functions

Autor:	Dayan, Alberto, Llinares, Adrián, Perfekt, Karl-Mikael
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Mathematics - Functional Analysis 46E30 (Primary) 30E05 30H30 42A61 47B38 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We characterize the restrictions of B\'ekoll\'e--Bonami weights of bounded hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a discrete version of Wolff's original theorem, by characterizing the trace of $BMO$-functions onto interpolating sequences. We consider an analogous question in our setting, by studying the trace of Bloch functions. Through Makarov's probabilistic approach to the Bloch space, our question can be recast as a restriction problem for dyadic martingales with uniformly bounded increments. Comment: Some minor changes have been made
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.04859 Zobrazit plný text záznamu View this record from Arxiv