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


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

JOURNAL OF MATHEMATICAL INEQUALITIES, vol.5, no.4, pp.491-506, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.7153/jmi-05-43
  • Title of Journal : JOURNAL OF MATHEMATICAL INEQUALITIES
  • 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).