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Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable...

Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality.

Jacek Dziubanski, Jacek Zienkiewicz (1999)

Revista Matemática Iberoamericana

Let {Tt}t>0 be the semigroup of linear operators generated by a Schrödinger operator -A = Δ - V, where V is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space HA1 by means of a maximal function associated with the semigroup {Tt}t>0. Atomic and Riesz transforms characterizations of HA1 are shown.

Hardy spaces and the Dirichlet problem on Lipschitz domains.

Carlos E. Kenig, Jill Pipher (1987)

Revista Matemática Iberoamericana

Our concern in this paper is to describe a class of Hardy spaces Hp(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ Rn when n ≥ 3, and a certain smooth counterpart of Hp(D) on Rn-1, by providing an atomic decomposition and a description of their duals.

Hardy spaces associated with some Schrödinger operators

Jacek Dziubański, Jacek Zienkiewicz (1997)

Studia Mathematica

For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy H A 1 space associated with A. An atomic characterization of H A 1 is shown.

Hardy spaces H¹ for Schrödinger operators with certain potentials

Jacek Dziubański, Jacek Zienkiewicz (2004)

Studia Mathematica

Let K t t > 0 be the semigroup of linear operators generated by a Schrödinger operator -L = Δ - V with V ≥ 0. We say that f belongs to H ¹ L if | | s u p t > 0 | K t f ( x ) | | | L ¹ ( d x ) < ∞ . We state conditions on V and K t which allow us to give an atomic characterization of the space H ¹ L .

Hardy spaces of conjugate temperatures

Martha Guzmán-Partida (1997)

Studia Mathematica

We define Hardy spaces of pairs of conjugate temperatures on ℝ + 2 using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.

Hausdorff operator on Morrey spaces and Campanato spaces

Jianmiao Ruan, Dashan Fan, Hongliang Li (2020)

Czechoslovak Mathematical Journal

We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

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