We investigate the boundedness of the maximal operator, the fractional maximal operator, and the fractional integral operator within the framework of weighted Morrey spaces. In particular, we consider the endpoint cases. This result can be recognized as the endpoint case of two weight multilinear norm inequality [4, Theorem 3.3] and, as a special case, recovers the Olsen inequality with small parameters [9, Examples 4.7].
"Note on the integral operators in weighted Morrey spaces." Hokkaido Math. J. 48 (2) 327 - 343, June 2019. https://doi.org/10.14492/hokmj/1562810512