We give new characterizations of the optimal data space for the L p (bD, σ)-Neumann boundary value problem for the ¯∂ operator associated to a bounded, Lipschitz domain D ⊂ C. We show that the solution space is embedded (as a Banach space) in the Dirichlet space and that for p = 2, the solution space is a reproducing kernel Hilbert space.
Gryc, W., Lanzani, L., Xiong, J., Zhang, Y. (2025). New Properties of Holomorphic Sobolev-Hardy Spaces. COMPLEX ANALYSIS AND OPERATOR THEORY, 19(1), 1-17 [10.1007/s11785-024-01637-8].
New Properties of Holomorphic Sobolev-Hardy Spaces
Loredana Lanzani
Membro del Collaboration Group
;
2025
Abstract
We give new characterizations of the optimal data space for the L p (bD, σ)-Neumann boundary value problem for the ¯∂ operator associated to a bounded, Lipschitz domain D ⊂ C. We show that the solution space is embedded (as a Banach space) in the Dirichlet space and that for p = 2, the solution space is a reproducing kernel Hilbert space.File in questo prodotto:
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