Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 3: 369 - 378

DOI: https://doi.org/10.1007/s11464-010-0061-1

Research articles

Rough bilinear fractional integrals with variable kernels

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  • 1.Department of Mathematics, Zhejiang University, Hangzhou 310027, China; 2.Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53217, USA;

Published date: 05 Sep 2010

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Abstract

We study the rough bilinear fractional integral "Graphic" where 0<α<n, Ω is homogeneous of degree zero on the y variable and satisfies "Graphic" for some s≥1, and Sn−1 denotes the unit sphere of "Graphic"ℝn. By assuming size conditions on Ω, we obtain several boundedness properties of "Graphic":"Graphic" where "Graphic" Our result extends a main theorem of Y. Ding and C. Lin [Math. Nachr., 2002, 246―247: 47―52].

Key words： Bilinear operator; multilinear fractional integral; variable kernel

Cite this article

Jiecheng CHEN, Dashan FAN, . Rough bilinear fractional integrals with variable kernels[J]. Frontiers of Mathematics in China, 2010 , 5(3) : 369 -378 . DOI: 10.1007/s11464-010-0061-1

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