The operator L^{-alpha/2} is bounded from M^{p, n-alpha p} to BMO_L and from VM^{p, n-alpha p} to VMO_L for 1 <= p < n/alpha, with an additional mapping from L^{p, infty} to BMO_L when p = n/alpha.
Samko,Maximal, potential and singular operators in vanishing generalized Morrey spaces, J
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Some new estimates for generalized fractional integrals associated with operators on Morrey spaces
The operator L^{-alpha/2} is bounded from M^{p, n-alpha p} to BMO_L and from VM^{p, n-alpha p} to VMO_L for 1 <= p < n/alpha, with an additional mapping from L^{p, infty} to BMO_L when p = n/alpha.