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Part of the book series: Progress in Mathematics ((PM,volume 346))

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Abstract

In order to extend the operator theory for L to Hardy spaces, we need to guarantee that certain operators f(L) preserve vanishing zeroth moments or have the conservation property f(L)c = c whenever c is a constant. In absence of integral kernels, the action of such operators on constants is explained via off-diagonal estimates. We discuss several conservation properties, in particular for resolvents and Poisson semigroups.

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References

  1. P. Auscher, S. Stahlhut, Functional calculus for first order systems of Dirac type and boundary value problems. Mém. Soc. Math. Fr. (N.S.) (144), vii+ 164 (2016)

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  2. E.M. Ouhabaz, Analysis of Heat Equations On Domains, volume 31 of London Mathematical Society Monographs Series (Princeton University Press, Princeton, 2005)

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  3. A. Rosén, Layer potentials beyond singular integral operators. Publ. Mat. 57(2), 429–454 (2013)

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Auscher, P., Egert, M. (2023). Conservation Properties. In: Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure. Progress in Mathematics, vol 346. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-29973-5_5

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