On embeddings of total Morrey spaces associated with Bessel operators

Let (0, ) and := -d 2 dx 2 -2+1 x d dx be the Bessel operator on R + := (0, ).In this paper, we study some embeddings into the total Morrey space L p,, (R + , dm ), 0 , < 2 + 2 associated with the Bessel operator on R + .These spaces generalize the Morrey space associated with the Bessel operator on R + so that L p, (R + , dm ) L p,, (R + , dm ) and the modified Morrey spaces associated with the Bessel operator on R + so that L p, (R + , dm ) L p,,0 (R + , dm ).