We introduce a space DHH =D（R2） H2H1D（R2）, where D（R2） is the testing function space whose functions are infinitely differentiable and have bounded support, and H2H1D（R2） is the space the double Hilbert tra...We introduce a space DHH =D（R2） H2H1D（R2）, where D（R2） is the testing function space whose functions are infinitely differentiable and have bounded support, and H2H1D（R2） is the space the double Hilbert transform acting on the testing function space. We prove that the double Hilbert transform is a homeomorphism from DHH onto itself.展开更多
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11071250, 11271162, 11126149）.
文摘We introduce a space DHH =D（R2） H2H1D（R2）, where D（R2） is the testing function space whose functions are infinitely differentiable and have bounded support, and H2H1D（R2） is the space the double Hilbert transform acting on the testing function space. We prove that the double Hilbert transform is a homeomorphism from DHH onto itself.
