Boundedness of some classical operators in Bourgain-Morrey spaces

Nouffou Diarra; Pokou  Nagacy

doi:10.62918/hjma.v2i2.22

Authors

Nouffou Diarra Université Felix Houphouët Boigny
Pokou Nagacy Laboratoire des Sciences et Technologies de l’Environnement, UFR Environnement, Université Jean Lorougnon Gu´ed´é

DOI:

https://doi.org/10.62918/hjma.v2i2.22

Keywords:

Bourgain-Morrey spaces, Wiener amalgam spaces, Maximal operators, sublinear operators and their commutators, Fourier transform, Riesz potential operator

Abstract

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.

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