The minimal operator and the John--Nirenberg theorem for weighted grand Lebesgue spaces
Volume 229 / 2015
Studia Mathematica 229 (2015), 189-202 MSC: Primary 42B25; Secondary 46E30. DOI: 10.4064/sm8070-1-2016 Published online: 12 January 2016
We introduce the minimal operator on weighted grand Lebesgue spaces, discuss some weighted norm inequalities and characterize the conditions under which the inequalities hold. We also prove that the John–Nirenberg inequalities in the framework of weighted grand Lebesgue spaces are valid provided that the weight function belongs to the Muckenhoupt $A_p$ class.