Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces

• Autores: Amiran Gogatishvili , Rza Mustafayev
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 1, 2012, págs. 11-28
• Idioma: inglés
• DOI: 10.1007/s13348-010-0012-x
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we find the condition on function ω which ensures the equivalence of norms of the Riesz potential and the fractional maximal function in generalized Morrey spaces {{\mathcal M}_{p,\omega}(\mathbb R^n)}.

• Referencias bibliográficas
  • Adams D.R.: A note on Riesz potentials. Duke Math. 42, 765–778 (1975)
  • Adams D.R., Xiao J.: Nonlinear potential analysis on Morrey spaces and their capacities. Indiana Univ. Math. J. 53(6), 1629–1663 (2004)
  • Bennett C., Sharpley R.: Interpolation of operators, Pure and Applied Mathematics, vol. 129, xiv+469 pp. Academic Press, Inc., Boston...
  • Burenkov, V.I., Gogatishvili, A., Guliyev, V.S., Mustafayev, R.Ch.: Boundedness of the Riesz Potential in Local Morrey-Type Spaces. Potential...
  • Burenkov V.I., Gogatishvili A., Guliyev V.S., Mustafayev R.Ch.: Boundedness of the fractional maximal operator in Morrey-type spaces. Complex...
  • Burenkov V.I., Guliyev H.V.: Necessary and sufficient conditions for boundedness of the maximal operator in the local Morrey-type spaces....
  • Carro M., Gogatishvili A., Martin J., Pick L.: Weighted inequalities involving two Hardy operators with applications to embeddings of function...
  • Evans W.D., Gogatishvili A., Opic B.: The reverse Hardy inequality with measures. Math. Inequal. Appl. 11(1), 43–74 (2008)
  • Gogatishvili A., Opic B., Pick L.: Weighted inequalities for Hardy-type operators involving suprema. Collect. Math. 57(3), 227–255 (2006)
  • Grafakos L.: Modern Fourier Analysis, 2nd edn, pp. 518. Springer, New York (2009)
  • Morrey C.B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43, 126–166 (1938)
  • Opic, B., Kufner, A.: Hardy-type inequalities. Pitman Research Notes in Mathematics Series, 219. Longman Scientific & Technical, Harlow...