Journal of the Australian Mathematical Society

Research Article

MORREY SPACES AND FRACTIONAL OPERATORS

HITOSHI TANAKAa1

a1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku Tokyo 153-8914, Japan (email: htanaka@ms.u-tokyo.ac.jp)

Abstract

The relation between the fractional integral operator and the fractional maximal operator is investigated in the framework of Morrey spaces. Applications to the Fefferman–Phong and the Olsen inequalities are also included.

(Received February 20 2009)

(Accepted September 01 2009)

2000 Mathematics subject classification

  • primary 42B35; secondary 42B25

Keywords and phrases

  • fractional integral operator;
  • fractional maximal operator;
  • Morrey space;
  • vector-valued inequality