An Atomic Representation for Bicomplex Hardy Classes

Abstract

We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that are representable by an atomic decomposition, and we show continuity of the Hilbert transform on this class of distributional boundary values.

Many typographical/notational errors corrected from the last version

References in corpus (4)

• Hardy spaces of the conjugate Beltrami equation
• Transmutation operators and complete systems of solutions for the radial Bicomplex Vekua equation
• An atomic representation for Hardy classes of solutions to nonhomogeneous Cauchy-Riemann equations
• Hardy Spaces of Meta-Analytic Functions and the Schwarz Boundary Value Problem