A simple real-variable proof that the Hilbert transform is an L-2-isometry

作者：Laeng Enrico^*

来源：Comptes Rendus Mathematique, 2010, 348(17-18): 977-980.

DOI：10.1016/j.crma.2010.07.002

The Hilbert transform H can be extended to an isometry of L-2. We prove this fact working directly on the principal value integral, completely avoiding the use of the Fourier transform and the use of orthogonal systems of functions. Our approach here is a byproduct of our attempts to understand the rearrangement properties of H.

• 出版日期2010-9