Skip to content

Advertisement

  • Research Article
  • Open Access

On the -Boundedness of Nonisotropic Spherical Riesz Potentials

Journal of Inequalities and Applications20072007:036503

https://doi.org/10.1155/2007/36503

  • Received: 20 November 2006
  • Accepted: 1 March 2007
  • Published:

Abstract

We introduced the concept of nonisotropic spherical Riesz potential operators generated by the -distance of variable order on -sphere and its -boundedness were investigated.

Keywords

  • Variable Order
  • Potential Operator
  • Riesz Potential
  • Riesz Potential Operator

[12345678910111213]

Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science and Arts, Kocatepe University, Afyon, 03200, Turkey

References

  1. Besov OV, Il'in VP, Lizorkin PI: The -estimates of a certain class of non-isotropically singular integrals. Doklady Akademii Nauk SSSR 1966, 169: 1250–1253.MathSciNetGoogle Scholar
  2. Çınar İ: The Hardy-Littlewood-Sobolev inequality for non-isotropic Riesz potentials. Turkish Journal of Mathematics 1997,21(2):153–157.MathSciNetMATHGoogle Scholar
  3. Çınar İ, Duru H: The Hardy-Littlewood-Sobolev inequality for -distance Riesz potentials. Applied Mathematics and Computation 2004,153(3):757–762. 10.1016/S0096-3003(03)00671-4MathSciNetView ArticleMATHGoogle Scholar
  4. Gadjiev AD, Dogru O: On combination of Riesz potentials with non-isotropic kernels. Indian Journal of Pure and Applied Mathematics 1999,30(6):545–556.MathSciNetMATHGoogle Scholar
  5. Sarikaya MZ, Yıldırım H: The restriction and the continuity properties of potentials depending on -distance. Turkish Journal of Mathematics 2006,30(3):263–275.MathSciNetMATHGoogle Scholar
  6. Sarikaya MZ, Yıldırım H: On the -spherical Riesz potential generated by the -distance. International Journal of Contemporary Mathematical Sciences 2006,1(2):85–89.MathSciNetMATHGoogle Scholar
  7. Sarikaya MZ, Yıldırım H: On the non-isotropic fractional integrals generated by the -distance. Selçuk Journal of Applied Mathematics 2006,7(1):17–23.MATHGoogle Scholar
  8. Sarikaya MZ, Yıldırım H: On the Hardy type inequality with non-isotropic kernels. Lobachevskii Journal of Mathematics 2006, 22: 47–57.MathSciNetMATHGoogle Scholar
  9. Sarikaya MZ, Yıldırım H, Ozkan UM: Norm inequalities with non-isotropic kernels. International Journal of Pure and Applied Mathematics 2006,31(3):337–344.MathSciNetMATHGoogle Scholar
  10. Stein EM: Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30. Princeton University Press, Princeton, NJ, USA; 1970:xiv+290.Google Scholar
  11. Zhou Z, Hong Y, Zhou CZ: The-boundedness of Riesz potential operators of variable order on a sphere. Journal of South China Normal University 1999, (2):20–24.Google Scholar
  12. Yıldırım H: On generalization of the quasi homogeneous Riesz potential. Turkish Journal of Mathematics 2005,29(4):381–387.MathSciNetMATHGoogle Scholar
  13. Sadosky C: Interpolation of Operators and Singular Integrals, Monographs and Textbooks in Pure and Applied Math.. Volume 53. Marcel Dekker, New York, NY, USA; 1979:xii+375.Google Scholar

Copyright

Advertisement