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…
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…
Riesz transform on manifolds and heat kernel regularity
- P. Auscher, T. Coulhon, X. Duong, S. Hofmann
- Mathematics
- 1 November 2004
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,…
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…
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…
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…
Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
- S. Hofmann, M. Mitrea, Michael 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…
The Dirichlet problem for parabolic operators with singular drift terms
- S. Hofmann, John L. Lewis
- Mathematics
- 2001
The Dirichlet problem and parabolic measure Absolute continuity and the $L^p$ Dirichlet problem: Part 1 Absolute continuity and the $L^p$ Dirichlet problem: Part 2.
Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains
- S. Hofmann, M. Mitrea, Michael Taylor
- Mathematics
- 15 December 2009
We develop the theory of layer potentials and related singular integral operators as a tool to study a variety of elliptic boundary problems on a family of domains introduced by Semmes [105, 106] and…
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