Weak type (p,p) estimates for Riesz transforms

By Sönke Blunck, P. Kunstmann. 2004

65 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c106e1e795eb54cd4642b487e368a5ed0d01896

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Classes of Hardy spaces associated with operators, duality theorem and applications (2008, unknown): “See [6] and [24].”
Generalized Gaussian estimates and the Legendre transform (2005, background): “calculus [6], maximal regularity [5] and Riesz transforms [ 7 ], [18].”
Riesz Transforms of Schrödinger Operators on Manifolds (2012, unknown): “The proof is based on techniques from Auscher [2] and Blunck and Kunstmann [8] and [9] together with Lp − Lq off-diagonal estimates for both of the semigroup e−t(−∆+V ) and its gradient.”
Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010, background): “ such that (1.5) ∇L−1/2 : Lp(Rn) −→Lp(Rn) ⇐⇒ p −(L) <p <2 +ε(L), (given (1.4) as a starting point, (1.5) with p−(L) <2n/(n + 2) is established by combining the results and methods of [39] or [18] with those of [6]; see also [5], [13], Chapter 4 of [14], and [17] for related theory). Moreove”
On necessary and sufficient conditions for $L^p$-estimates of Riesz transforms associated to elliptic operators on $\RR^n$ and related estimates (2005, unknown): “6 This follows by combining works of Blunck & Kunstmann [ BK2 , Proposition 2.3] and”
Riesz transform and related inequalities on non‐compact Riemannian manifolds (2003, background): “For variations on the proof as well as interesting generalizations, see [ 7 , 39]; for extensions to vector bundles, see [44]; and for an H 1 theory, see [34].”
Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, background): “In fact, this criterion is in the air in [Fef] but, still, [BK1] brings some novelty such as the removal of the mean value property already observed in [DMc] when p = 1. See also [ BK2 ] and [HM] for Lp bounds p < 2 of the Riesz transforms of elliptic operators starting from the L2 bound proved in [”
Hardy and BMO spaces associated to divergence form elliptic operators (2006, unknown): “In fact, we also know that there exists pL, 1 ≤ pL < 2n/(n + 2), such that the Riesz transform is bounded in L(R) for pL < p ≤ 2 (see [21], [11], [3], [9], [10] and §2 for more details; see also [12] for related theory).”
Orlicz-Hardy spaces associated with operators (2009, background): “Kunstmann [ 22 ] and Hofmann and Martell [23] . Remark 2.1.”
The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients (2013, result): “It seems very likely that L-boundedness for some restricted range of p should still hold, even in the absence of DG/N/M, as is true in the special case of the ‘block matrices’ treated in [3, 11, 28, 41], but we have not considered this question here.”
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, unknown): “ic operators (−1)m X |α|=m=|β| ∂β (a α,β∂ α) interpreted inthe usualweak sensevia a sesquilinear form, with complex bounded measurable coeﬃcients aα,β for all multi-indices α and β (see, for example, [10, 18]); (iii) the Schro¨dinger operator −∆ + V on Rn with the nonnegative potential V ∈ L1 loc(R ”
Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates (2011, result): “We conclude this introduction by remarking that this work, as well as the earlier cited papers [DY1], [DY2], [AMR], and [HM], can in some sense be viewed as a companion to the Lp theory developed for general classes of operators in [ BK1 ],[BK2], [HMa] and [Au].”