Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 92470, 16 pages
doi:10.1155/JIA/2006/92470

Limiting case of the boundedness of fractional integral operators on nonhomogeneous space

Yoshihiro Sawano,1 Takuya Sobukawa,2 and Hitoshi Tanaka1

 1Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
2Department of Mathematics Education, Faculty of Education, Okayama University, 3-1-1 Tsushima-naka, Okayama 700-8530, Japan
Received 13 April 2006; Accepted 12 June 2006

Abstract

We show the boundedness of fractional integral operators by means of extrapolation. We also show that our result is sharp.