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Hardy and BMO spaces associated to divergence form elliptic operators

- S. Hofmann, S. Mayboroda
- Mathematics
- 27 November 2006

Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie… Expand

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates

- S. Hofmann, G. Lu, D. Mitrea, M. Mitrea, Lixin Yan
- Mathematics
- 29 October 2011

Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy… Expand

Riesz transform on manifolds and heat kernel regularity

- P. Auscher, T. Coulhon, X. Duong, S. Hofmann
- Mathematics
- 1 November 2004

Abstract One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is L p bounded on… Expand

The solution of the Kato square root problem for second order elliptic operators on Rn

- P. Auscher, S. Hofmann, M. Lacey, A. Mcintosh, P. Tchamitchian
- Mathematics
- 1 September 2002

We prove the Kato conjecture for elliptic operators on Jfin. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator L =-div (AV) with bounded… Expand

The Green function estimates for strongly elliptic systems of second order

- S. Hofmann, Seick Kim
- Mathematics
- 11 April 2007

We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain $$\Omega \subseteq {\mathbb{R}}^n,… Expand

Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces

- S. Hofmann, S. Mayboroda, A. Mcintosh
- Mathematics
- 3 February 2010

Let L be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with L, such as the heat semigroup and Riesz transform, are… Expand

Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$

- S. Hofmann, J. M. Martell
- Mathematics
- 17 February 2012

We present a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, we establish scale invariant absolute continuity of harmonic measure with respect… Expand

Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains

- S. Hofmann, M. Mitrea, Michael E. Taylor
- Mathematics
- 1 December 2007

In the first part of this article we give intrinsic characterizations of the classes of Lipschitz and C1 domains. Under some mild, necessary, background hypotheses (of topological and geometric… Expand

A local Tb Theorem for square functions

- S. Hofmann
- 2011

We prove a “local” Tb Theorem for square functions, in which we assume only Lq control of the pseudo-accretive system, with q > 1. We then give an application to variable coefficient layer potentials… Expand

Lp bounds for Riesz transforms and square roots associated to second order elliptic operators

- S. Hofmann, J. M. Martell
- Mathematics
- 1 July 2003

We consider the Riesz transforms ∇L−1/2, where L≡− divA(x)∇, and A is an accretive, n × n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on… Expand

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