关键词: 双Hilbert变换, 分数阶双Hilbert变换, 混合范数

Abstract: In this work, we investigate the boundedness of the double Hilbert transform on the endpoint of the mixed-norm Lebesgue spaces. We also give the boundedness of the fractional double Hilbert transform on mixed Lebesgue spaces for the general cases, and then especially on one kind of endpoint cases.

Key words: double Hilbert transform, fractional double Hilbert transform, mixed-norm