Abstract
In this chapter, we work out a precise relation between kernel bounds and critical numbers p−(L) strictly below 1. Except for Sect. 14.5 this is an intermezzo not needed for the application to boundary value problems. However, it nicely illustrates the usefulness of our choice for the interval J (L) compared to Auscher (Mem Am Math Soc 186(871):xviii+75, 2007) and connects with the theory of Gaussian estimates in the first chapter of Auscher and Tchamitchian (Astérisque (249):viii+172, 1998). In particular, we obtain resolvent kernels from those of high powers of the resolvent without using heat semigroups (which exist only if ωL < π∕2).
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Auscher, P., Egert, M. (2023). Critical Numbers and Kernel Bounds. 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_14
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DOI: https://doi.org/10.1007/978-3-031-29973-5_14
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