Hardy spaces and divergence operators on strongly Lipschitz domains of Rn

By P. Auscher, E. Russ. 2002

130 citations recorded by the source corpus.

Abstract Let Ω be a strongly Lipschitz domain of R n . Consider an elliptic second-order divergence operator L (including a boundary condition on ∂Ω ) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L1. Under suitable assumptions on L, we identify this maximal Hardy space with H 1 ( R n ) if Ω= R n , with H r 1 (Ω) under the Dirichlet boundary condition, and with H z 1 (Ω) under the Neumann boundary condition.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f4560998a57f53e87a6ba16ad73722e14aac826e

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In Applied Mathematics

Citations in the corpus

Hardy Spaces of Differential Forms on Riemannian Manifolds (2006, background): “4) is inspired by the one of Proposition 7 in [2] where the Poisson semigroup is changed to the heat semigroup.”
Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, background): “ces on Rn is intimately connected with the Laplacian operator. In recent years, the study of Hardy spaces and BMO spaces associated with diﬀerent operators inspires great interests; see, for example, [1, 2, 3, 11, 12, 13, 14, 15, 19, 18, 23, 31] and their references. In [1], Auscher, Duong and McInt”
Classes of Hardy spaces associated with operators, duality theorem and applications (2008, unknown): “In [3] and [2], the Hardy space associated with an elliptic second-order divergence operator L was introduced by using the Poisson semigroup of L.”
Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010, background): “Besides the aforementioned works [10] and [39], some properties of the Hardy and BMO spaces associated with different operators were introduced previously in [11], [25], [26], [60].”
New Abstract Hardy Spaces (2007, background): “ dual BMO for p tends to ∞. 2 However, there are situations where H1 CW(X) is not the right substitute to L1(X) and there has been recently a number of works with goal to deﬁne an adapted Hardy space [1, 2, 8, 20, 17, 19, 21, 18, 22, 27]. For example H1 CW(X) is not well adapted to operators such as”
Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, methodology): “We prove this lemma by borrowing some ideas from [8, 7, 95].”
New Orlicz–Hardy spaces associated with divergence form elliptic operators (2009, background): “In this section, we recall some notions and notation on the divergence form elliptic operator, and present some basic properties on Orlicz functions and also describe some basic assumptions on them.”
Calderón reproducing formulas and new Besov spaces associated with operators (2012, methodology): “We will develop the theme in the works [17,18,1,2] and define the Besov norm Ḃ p,q via quadratic norms of L.”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “l theory, we typically ﬁnd BMO spaces associated to a metric or a martingale ﬁltration. Recently, Duong and Yan [25, 26] have extended the theory to certain semigroups of positive operators, see also [4, 36]. However, they still impose the existence of a metric in the underlying space, something tha”