Bandaliyev R. A.
Ukr. Mat. Zh. - 2017. - 69, № 11. - pp. 1443-1454
The main goal of this paper is to prove a two-weight boundedness for Riesz potential from one weighted Banach function space to another weighted Banach function space. In particular, we obtain a two-weight boundedness for Riesz potential and find sufficient conditions on the weights for boundedness of Riesz potential in weighted Musielak – Orlicz spaces.
Two-Weight Criteria for the Multidimensional Hardy-Type Operator in $p$-Convex Banach Function Spaces and Some Applications
Ukr. Mat. Zh. - 2015. - 67, № 3. - pp. 313-325
The main aim of the paper is to prove a two-weight criterion for the multidimensional Hardy-type operator from weighted Lebesgue spaces into p-convex weighted Banach function spaces. The problem for the dual operator is also considered. As an application, we prove a two-weight criterion of boundedness of the multidimensional geometric mean operator from weighted Lebesgue spaces into weighted Musielak–Orlicz spaces.