Discrete Hardy Spaces

作者：Cerejeiras Paula^*; Kaehler Uwe; Ku Min; Sommen Frank

来源：Journal of Fourier Analysis and Applications, 2014, 20(4): 715-750.

DOI：10.1007/s00041-014-9331-8

• Discrete Dirac operator
• Discrete Cauchy transform
• Discrete monogenic functions
• Hardy space

We study the boundary behavior of discrete monogenic functions, i.e. null-solutions of a discrete Dirac operator, in the upper and lower half space. Calculating the Fourier symbol of the boundary operator we construct the corresponding discrete Hilbert transforms, the projection operators arising from them, and discuss the notion of discrete Hardy spaces. Hereby, we focus on the 3D-case with the generalization to the n-dimensional case being straightforward.

• 出版日期2014-8