Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 092470, 16 pages

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

Copyright © 2006 Yoshihiro Sawano et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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