Some new function spaces and their applications to Harmonic analysis

Coifman, Ronald R.; Meyer, Yves; Stein, Elias M.

doi:10.1016/0022-1236(85)90007-2

Cited by 440 publications

(499 citation statements)

References 10 publications

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“…Lemma 2.1 ( [14]) Fix some α > 0. There exists γ ∈ (0, 1), sufficiently close to 1, such that for every closed set F whose complement has finite measure and every non-negative function Φ the following inequality holds:…”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…The ideas in this proof go back to the decomposition of the tent spaces in [14] as well as to the atomic decomposition of the classical Hardy spaces (see [31]). …”

Section: Lemma 43 We Have the Containments Hmentioning

confidence: 99%

“…We shall require some rather extensive preliminaries. In particular, we shall use the "tent space" approach of Coifman-Meyer-Stein [14]. Let us now recall the basic theory.…”

Section: Lemma 73 Definementioning

confidence: 99%

“…Define the tent spaces 22) and 23) and recall from [14] that (T 1 (R n+1 + )) * = T ∞ (R n+1 + ). We now prove the following analogue of a classical estimate of [19].…”

Section: Lemma 73 Definementioning

confidence: 99%

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Hardy and BMO spaces associated to divergence form elliptic operators

2008

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Section: Notation and Preliminariesmentioning

confidence: 99%

“…The ideas in this proof go back to the decomposition of the tent spaces in [14] as well as to the atomic decomposition of the classical Hardy spaces (see [31]). …”

Section: Lemma 43 We Have the Containments Hmentioning

confidence: 99%

“…We shall require some rather extensive preliminaries. In particular, we shall use the "tent space" approach of Coifman-Meyer-Stein [14]. Let us now recall the basic theory.…”

Section: Lemma 73 Definementioning

confidence: 99%

“…Define the tent spaces 22) and 23) and recall from [14] that (T 1 (R n+1 + )) * = T ∞ (R n+1 + ). We now prove the following analogue of a classical estimate of [19].…”

Section: Lemma 73 Definementioning

confidence: 99%

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Hardy and BMO spaces associated to divergence form elliptic operators

2008

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“…Using (2.5) and (2.3) it is easy to see We can do this via duality [1], testing F against g such that , the proof of (3.13) is complete.…”

Section: Lemma 311mentioning

confidence: 99%

Elliptic equations in the plane satisfying a Carleson measure condition

Dindoš¹,

Rule²

2010

Rev. Mat. Iberoam.

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In this paper we settle (in dimension n = 2) the open question whether for a divergence form equation div(A∇u) = 0 with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the L p Neumann and Dirichlet regularity problems are solvable for some values of p ∈ (1, ∞). The related question for the L p Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

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Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

Dindoš

Pipher

Rule³

2016

Comm Pure Appl Math

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Let Ω be a Lipschitz domain in ℝn,n≥2, and L=div A∇ be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in H1,p(∂Ω) and of the Neumann problem with Lp(∂Ω) data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the H1,p(∂Ω) Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc.

show abstract

Some new function spaces and their applications to Harmonic analysis

Cited by 440 publications

References 10 publications

Hardy and BMO spaces associated to divergence form elliptic operators

Hardy and BMO spaces associated to divergence form elliptic operators

Elliptic equations in the plane satisfying a Carleson measure condition

Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

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