On the Riesz potential in Morrey spaces, associated with the Laplace-Bessel differential operator


Zeren Y.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol.19, no.8, pp.607-612, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 8
  • Publication Date: 2008
  • Doi Number: 10.1080/10652460802030524
  • Title of Journal : INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Page Numbers: pp.607-612

Abstract

We consider the generalized shift operator, associated with the Laplace-Bessel differential operator Delta(B) = Sigma(n)(i=1) (partial derivative(2)/partial derivative x(i)(2)) + (gamma/x(n)) (partial derivative(2)/partial derivative x(n)). We study the Riesz potential I(gamma)(alpha) (B-Riesz potential), associated with the generalized shift operator (B-Riesz potential) and its modified version (I) over tilde (alpha)(gamma) (modified B-Riesz potential) in the B-Morrey space. We prove that the operator (I) over tilde (alpha)(gamma), 0 < alpha < n + gamma is bounded from L(1,n+gamma-alpha,gamma)(R(+)(n)) to BMO(gamma)(R(+)(n)).