We study the weighted norm inequality of -type,
along with its weak-type analogue, for , where is an integral operator associated with the nonnegative kernel on . Here denotes the class of positive Radon measures in ; , and .
For both weak-type and strong-type inequalities, we provide conditions which characterize the measures for which such an embedding holds. The strong-type -inequality for is closely connected with existence of a positive function such that , i.e., a supersolution to the integral equation
This study is motivated by solving sublinear equations involving the fractional Laplacian,
in domains which have a positive Green function for .
"A sublinear version of Schur's lemma and elliptic PDE." Anal. PDE 11 (2) 439 - 466, 2018. https://doi.org/10.2140/apde.2018.11.439