Journal of Operator Theory

Volume 68, Issue 1, Summer 2012 pp. 3-17.

Fractional integral operators on weighted anisotropic Hardy spaces

Authors: Sen-Hua Lan (1), Ming-Yi Lee (2), and Chin-Cheng Lin (3)
Author institution: (1) Department of Mathematics, Lishui University, Lishui, Zhejiang 323000, China
(2) Department of Mathematics, National Central University, Chung-Li 320, Taiwan
(3) Department of Mathematics, National Central University, Chung-Li 320, Taiwan

Summary: In this article we study the fractional integral operators associated with anisotropic setting. We derive weighted norm inequalities for these operators on weighted anisotropic $H^p$ spaces and weighted $L^p$ spaces.

Keywords: $\mathcal A_p$ weight, anisotropic Hardy space, fractional integral operator,\break Hardy--Littlewood--Sobolev inequality

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