Harmonic Besov spaces with small exponents
\"Omer Faruk Do\u{g}an

TL;DR
This paper investigates harmonic Besov spaces with small exponents on the unit ball, providing characterizations, duality relations, and boundary growth properties, advancing understanding of these function spaces.
Contribution
It introduces new characterizations and duality results for harmonic Besov spaces with exponents less than one, including growth and atomic decomposition insights.
Findings
Dual of $b^p_eta$ is weighted Bloch space under certain pairings
Characterizations via derivatives and differential operators
Results on boundary growth and atomic decomposition
Abstract
We study harmonic Besov spaces on the unit ball of , where and . We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that are more compatible with reproducing kernels of harmonic Bergman-Besov spaces. We show that the dual of harmonic Besov space is weighted Bloch space under certain volume integral pairing for and . Our other results are about growth at the boundary and atomic decomposition.
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