MMN-5045
Bourgain-Lebesgue spaces
Baohua Dong; Xuanxuan Hu; Jingshi Xu;Abstract
Bourgain initially introduce a specific instance of Bourgain-Morrey spaces
to investigate the restriction and multiplier problems in $\mathbb{R}^3$.
Following this, the concept of Bourgain-type function spaces garnered considerable attention among researchers.
In the paper, we aim to introduce Bourgain-Lebesgue spaces
and delve into the embedding properties between Lebesgue spaces and the Bourgain-Lebesgue spaces.
Additionally, we explore the boundedness properties within Bourgain-Lebesgue spaces concerning local Hardy-Littlewood maximal operators and their vector-valued counterparts.
Vol. 27 (2026), No. 1, pp. 193-208