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

Abstract

We come back to the Riesz transform interval

$$\displaystyle \begin{aligned} \mathcal{I} (L) := \big \{ p \in (1_*,\infty ) : R_L \text{ is } a^{-1} \operatorname {H}^p - \operatorname {H}^p\text{ -bounded}\big \}, \end{aligned} $$

defined in (7.1), the endpoints of which we have denoted by r±(L). In Chap. 7 we have characterized the endpoints of the part of ℐ(L) in (1, ). The identification theorem for adapted Hardy spaces allows us to complete the discussion in the full range of exponents.

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References

  1. S. Hofmann, S. Mayboroda, A. McIntosh, Second order elliptic operators with complex bounded measurable coefficients in Lp, Sobolev and Hardy spaces. Ann. Sci. Éc. Norm. Supér. (4) 44(5), 723–800 (2011)

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Auscher, P., Egert, M. (2023). Riesz Transform Estimates: Part II. 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_11

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