Boundedness of some classical operators in Bourgain-Morrey spaces

Diarra, Nouffou
Nagacy, Pokou

Hilbert Journal of Mathematical Analysis
Vol. 2 No. 2 (2024): Hilbert J. Math. Anal.

In this paper, we establish relationships between the norms of both Bourgain-Morrey spaces and Wiener amalgam spaces. Therefore, we take advantage of these relations to study the action on Bourgain-Morrey spaces of some classical operators such as maximal operators, Hardy operators, some sublinear operators and their commutators, and the Fourier transform. We also establish in Bourgain-Morrey spaces a norm equivalence of Riesz potential and fractional maximal function.