Rough bilinear fractional integrals with variable
kernels

doi:10.1007/s11464-010-0061-1

Front. Math. China

2010, Vol. 5

Issue (3) : 369-378 https://doi.org/10.1007/s11464-010-0061-1

Research articles

Rough bilinear fractional integrals with variable kernels

Jiecheng CHEN¹,Dashan FAN²,

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

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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 S^n−1 denotes the unit sphere of "Graphic"

ℝn. By assuming size conditions on Ω, we obtain several boundedness properties of "Graphic"

where

Our result extends a main theorem of Y. Ding and C. Lin [Math. Nachr., 2002, 246―247: 47―52].

Keywords Bilinear operator multilinear fractional integral variable kernel

Issue Date: 05 September 2010

Cite this article:

Jiecheng CHEN,Dashan FAN. Rough bilinear fractional integrals with variable kernels[J]. Front. Math. China, 2010, 5(3): 369-378.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0061-1
https://academic.hep.com.cn/fmc/EN/Y2010/V5/I3/369

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[1]	Yanping CHEN, Liwei WANG. L²( $ℝ n$ ) boundedness for Calderón commutator with rough variable kernel[J]. Front. Math. China, 2018, 13(5): 1013-1031.

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