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

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Zeren Y.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol.19, no.8, pp.607-612, 2008 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 19 Issue: 8
• Publication Date: 2008
• Doi Number: 10.1080/10652460802030524
• Journal Name: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.607-612
• Yıldız Technical University Affiliated: No

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)).