We prove a weighted version of the Hardy–Littlewood–Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in this particular case.
"On weighted inequalities for fractional integrals of radial functions." Illinois J. Math. 55 (2) 575 - 587, Summer 2011. https://doi.org/10.1215/ijm/1359762403