On Lp estimates for square roots of second order elliptic operators on Rn.

By P. Auscher. 2004

48 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/92b8e30a676933267e0463db8abcdd6065862e12

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In Applied Mathematics

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Citations in the corpus

Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schr\ (2006, methodology): “His self-adjoint. For q6= 2, this is a consequence of the Gaussian estimates for the ke rnels of e−tH, t>0 (this was ﬁrst proved in [ADMc] using the vector-valued version of the work in [DMc]. See [Aus] for a more general argument in this spirit or [LeM] for an abstract proof relying on functiona”
New Abstract Hardy Spaces (2007, methodology): “(20) with the control |f| ≤ M HL,s(f). To prove this, we use the assumption that Mσ is bounded by MHL,2. In the proof of Theorem 5.3, we have used s = 2 however we can use the same arguments with s ∈ [1,2]. ⊓⊔ We have a second corollary (independent of Corollary 5.7) : Corollary 5.8 Assume that for ”
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).”
Riesz transform on manifols and Poincaré inequalities (2005, methodology): “7 in Section 1 uses methods of the first author in [1] adapted to the present situation and in particular a Calderón-Zygmund lemma for Sobolev functions, which allows us to do a Marcinkiewicz type interpolation.”
On necessary and sufficient conditions for $L^p$-estimates of Riesz transforms associated to elliptic operators on $\RR^n$ and related estimates (2005, unknown): “ter IV, Theorem 1, using [AMcT], Theorem 3.5 and [AHLMcT], Theorem 1.4. 51 The ﬁrst inequality is proved in [BK2], [HM] for the range 2n n+2 < p < 2 and the extension to this larger range is in [A], the second inequality is in [HM] for the range 2 < p < 2n n−2 , and in [A] for the rest o”
Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, methodology): “Such a decomposition is used is [2] in the Euclidean setting and a similar decomposition appear earlier in [14,20] for the purpose of real interpolation for Sobolev spaces.”