Bourgain-Morrey spaces and their applications to boundedness of operators
In this paper, the authors study the so-called Bourgain-Morrey spaces. Precisely, the authors study the fundamental properties of the Bourgain-Morrey space, including approximation and interpolation properties. Moreover, the boundedness of operators, such as the Hardy-Littlewood maximal operator, fractional integral operators, fractional maximal operators, and singular integral operators, on the Bourgain-Morrey space is also established. In particular, the embedding result by \textit{P. Bégout} and \textit{A. Vargas} [Trans. Am. Math. Soc. 359, No. 11, 5257--5282 (2007; Zbl 1171.35109)] is refined. Furthermore, the authors describe the dual of Bourgain-Morrey spaces and combine this with existing results to conclude the reflexivity of these spaces.
scientific article; zbMATH DE number 7616871
scientific article