The Hilbert transforms associated with monomial curves have a natural non-isotropic structure. We study the commutator of such and symbol $b$ prove upper bound this when is in corresponding BMO space by using Cauchy integral trick. also consider lower introducing new testing given curve, which shows that classical contained space. show non-zero curvature are important, since considering lines, ...

The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time-frquency analysis. Imaging and other applications to multidimensional signals call for extension of the method to higher dimensions. We justify the usage of partial Hilbert transforms to define multidimensional analytic signals from both engineering and mathematical persp...

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class...

In the present paper is proposed a numerical method to approximate Hilbert transforms of the type