双Hilbert变换与分数阶双Hilbert变换在混合范数空间上的有界性

Boundedness of double Hilbert transform and fractional double Hilbert transform on mixed Lebesgue spaces

研究双Hilbert变换在边界情况的具有混合范数Lebesgue空间上、分数阶双Hilbert变换在一般的具有混合范数Lebesgue空间上和在一种混合范数边界情况等3类有界性问题.

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.