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, cilt.5, ss.491-506, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 5 Konu: 4
  • Basım Tarihi: 2011
  • Doi Numarası: 10.7153/jmi-05-43
  • Dergi Adı: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Sayfa Sayıları: ss.491-506

Özet

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).