Abstract
In this chapter, we show that the critical numbers are intrinsic in the sense that we could have equivalently defined them through other families of functions of L than resolvents. We focus on the Poisson semigroup and, when a = 1, the heat semigroup.
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References
A. Amenta, P. Auscher, Elliptic Boundary Value Problems with Fractional Regularity Data, volume 37 of CRM Monograph Series (American Mathematical Society, Providence, 2018). The first order approach
P. Auscher, On necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on \(\mathbb {R}^n\) and related estimates. Mem. Am. Math. Soc. 186(871), xviii+ 75 (2007)
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Auscher, P., Egert, M. (2023). Critical Numbers for Poisson and Heat Semigroups. 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_12
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DOI: https://doi.org/10.1007/978-3-031-29973-5_12
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