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In this paper, the mean value formula depends on the Bessel-generalized shift operator corresponding to the solutions of the boundary value problem related to the multidimensional Bessel operator are studied. In addition, Riesz transforms R B related to the multidimensional Bessel operators are studied. Since a Bessel-generalized shift operator is a translation operator corresponding to the multidimensional Bessel operator, we construct a family of R B by using a Bessel-generalized shift operator. Finally, we analyze weighted inequalities involving R B . MSC: Primary 31B05; 35G10; secondary 34B30; 47F05

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