High order Riesz transforms and mean value formula for generalized translate operator


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EKİNCİOĞLU İ., SAYAN H. H., KESKİN C.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014 (SCI-Expanded) identifier identifier

Abstract

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.