Abstract
We develop a representation of the second kind for certain Hardy classes of solutions to nonhomogeneous Cauchy–Riemann equations and use it to show that boundary values in the sense of distributions of these functions can be represented as the sum of an atomic decomposition and an error term. We use the representation to show continuity of the Hilbert transform on this class of distributions and use it to show that solutions to a Schwarz-type boundary value problem can be constructed in the associated Hardy classes.
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Blair, W.L. An Atomic Representation for Hardy Classes of Solutions to Nonhomogeneous Cauchy–Riemann Equations. J Geom Anal 33, 307 (2023). https://doi.org/10.1007/s12220-023-01374-y
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DOI: https://doi.org/10.1007/s12220-023-01374-y
Keywords
- Hardy spaces
- Atomic decomposition
- Generalized analytic functions
- Nonhomogeneous Cauchy–Riemann equations
- Boundary value in the sense of distributions
- Hilbert transform
- Schwarz boundary value problem