|Title:||Ultradistributional boundary values of harmonic functions on the sphere||Journal:||Journal of Mathematical Analysis and Applications||Volume:||457||Issue:||1||First page:||533||Last page:||550||Issue Date:||1-Jan-2018||Rank:||M21||ISSN:||0022-247X||DOI:||10.1016/j.jmaa.2017.08.035||Abstract:||
We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calderón and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.
|Keywords:||Abel summability | Boundary values on the sphere | Harmonic functions on the unit ball | Partial derivatives of spherical harmonics | Support of ultradistributions | Ultradifferentiable functions||Publisher:||Elsevier||Project:||Ghent University, BOF-grant 01N01014|
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