Calderón-Zygmund theory for non-integral operators and the $H^{\infty}$ functional calculus

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Riesz transform on manifolds and heat kernel regularity (2004, background): “Then one can invoke a result in [35] if one wants a result for the full range 1< p< 2 or its generalization to a limited range p0 < p< 2 in [9].”
Riesz transform on manifolds and Poincaré inequalitie (2005, methodology): “To estimate the L2 norm, we follow ideas in [6, 19] and dualize against u ∈ L2(M,μ) with ‖u‖2 = 1 and write ∫”
Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010, methodology): “5) with p−(L) < 2n/(n + 2) is established by combining the results and methods of [38] or [16] with those of [7]; see also [6], [12], [13], [17] for related theory).”
Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “In the second step, we now use the extrapolation method of [Auscher 2007; Blunck and Kunstmann 2003] to show that T # is of weak type . p 0 ; p 0 / , which by interpolation with the L 2 -boundedness will conclude the proof of the proposition.”
Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem (2006, unknown): “(b) In [8, 9, 10, 11, 12], Blunck and Kunstmann develop spectral multiplier theorems for operators which generate semigroups without heat kernel acting on spaces satisfying the doubling condition.”