NECESSARY AND SUFFICIENT CONDITIONS FOR THE BOUNDEDNESS OF THE RIESZ POTENTIAL IN MODIFIED MORREY SPACES


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Guliyev V. S. , Hasanov J. J. , ZEREN Y.

JOURNAL OF MATHEMATICAL INEQUALITIES, vol.5, no.4, pp.491-506, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.7153/jmi-05-43
  • Journal Name: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.491-506
  • Keywords: Riesz potential, fractional maximal function, modified Morrey space, Hardy-Littlewood-Sobolev inequality, Schodinger type operator, WEIGHTED NORM INEQUALITIES, SCHRODINGER-OPERATORS

Abstract

We prove that the fractional maximal operator M-alpha and the Riesz potential operator I-alpha, 0 < alpha < n are bounded from the modified Morrey space (L) over tilde (1,lambda) (R-n) to the weak modified Morrey space W (L) over tilde (q,lambda) (R-n) if and only if, alpha/n <= 1 - 1/q <= alpha/(n - lambda) and from (L) over tilde (p,lambda) (R-n) to (L) over tilde (q,lambda) (R-n) if and only if, alpha/n <= 1/p - 1/q <= alpha/(n - lambda).