Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation

David, Guy; Journé, Jean-Lin; Semmes, Stephen

doi:10.4171/rmi/17

Cited by 277 publications

(297 citation statements)

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“…Even more recently, David and Journé, together with S. Semmes, extended this result to spaces of homogeneous type [15]. This represents, therefore, a unification of many of the ideas and results that are involved in this development of Harmonic Analysis that has taken place during the seventies and eighties.…”

Section: The Tl Theorem a Calderón-zygmund Operator T Is Bounded On mentioning

confidence: 96%

Book Review: Real variable methods in harmonic analysis

Weiss¹

1989

Bull. Amer. Math. Soc.

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Section: The Tl Theorem a Calderón-zygmund Operator T Is Bounded On mentioning

confidence: 96%

Book Review: Real variable methods in harmonic analysis

Weiss¹

1989

Bull. Amer. Math. Soc.

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“…In what follows, without loss of generality, we will always assume that Q x,k , Q x ,k and Q y,k are transit cubes. Now, let {S k } k∈Z be an approximation to the identity as in Definition 2.9 and [3] and [27], based on Coifman's idea, we can write (2.29)…”

Section: Lemma 24 There Exist a Sequence Of Operators Of {Smentioning

confidence: 99%

“…Also using this formula one can establish the embedding theorems, the interpolation theorems, duality, atomic decomposition and the T 1 theorems for the spacesḂ s pq (R d ); see [4,21,31,32] for more details. By Coifman's ideas, David, Journé and Semmes in [3] provided the LittlewoodPaley theory for spaces of homogeneous type introduced by Coifman and Weiss in [2]. To be precise, if {S k } ∞ k=−∞ is an approximation to the identity on a space of homogeneous type, then their kernels {S k (x, y)} ∞ k=1 satisfy certain size and regularity conditions; see [3] for the construction of such an approximation to the identity.…”

Section: Introductionmentioning

confidence: 99%

“…By Coifman's ideas, David, Journé and Semmes in [3] provided the LittlewoodPaley theory for spaces of homogeneous type introduced by Coifman and Weiss in [2]. To be precise, if {S k } ∞ k=−∞ is an approximation to the identity on a space of homogeneous type, then their kernels {S k (x, y)} ∞ k=1 satisfy certain size and regularity conditions; see [3] for the construction of such an approximation to the identity. It is worth pointing out that the doubling property plays an important role in this construction.…”

Section: Introductionmentioning

confidence: 99%

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Besov spaces with non-doubling measures

Deng¹,

Han

Yang

2005

Trans. Amer. Math. Soc.

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Abstract. Suppose that µ is a Radon measure on R d , which may be nondoubling. The only condition on µ is the growth condition, namely, there is a constant C 0 > 0 such that for all x ∈ supp (µ) and r > 0,where 0 < n ≤ d. In this paper, the authors establish a theory of Besov spaceṡ B s pq (µ) for 1 ≤ p, q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure µ, C 0 , n and d. The method used to define these spaces is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are obtained.

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“…Probably the conditions on the multilinear T 1 theorem can be further relaxed along the lines of the linear T b theorem of David, Journé, and Semmes [19].…”

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

On multilinear singular integrals of Calderón-Zygmund type

Grafakos

Torres²

2002

Publicacions Matemàtiques

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Abstract. A variety of results regarding multilinear Calderón-Zygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T 1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal operator associated with multilinear singular integrals is also introduced and employed to obtain weighted norm inequalities.

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Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation

Cited by 277 publications

References 0 publications

Book Review: Real variable methods in harmonic analysis

Book Review: Real variable methods in harmonic analysis

Besov spaces with non-doubling measures

On multilinear singular integrals of Calderón-Zygmund type

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