The Boundedness of Calderón-Zygmund Operators on the Spaces $\dot{F}^{\alpha, q}_p$

Frazier, Michael; Weiss, Guido; Torres, Rodolfo H.

doi:10.4171/rmi/63

Cited by 58 publications

(46 citation statements)

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“…This is quite different from the approaches in [7,8,10,11]. The proof of Theorem 1.1 depends on the Beylkin-Coifman-Rohklin wavelet decomposition of the operator 7.…”

Section: 2') S U P / (\K(xy)\ + \K(yx)\)dymentioning

confidence: 81%

“…(1.1') ( The 7(1) theorem has also been considered by Lemarie on the Besov spaces [10], Frazier et al on the Triebel-Lizorkin spaces [7], and Han and Hofmann on both classes of spaces [8]. The definitions of such spaces can be stated as follows (see [13]) : Let y(W) be the space of tempered test functions.…”

Section: I(7v F)\ < T N (\\mentioning

confidence: 99%

“…https://doi.org/10.1017/S1446788700010132 [7] Wavelet decomposition of Calderon-Zygmund operators 35…”

Section: T(l) Theorem On Besov Spacesmentioning

confidence: 99%

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Wavelet decomposition of Calderón-Zygmund operators on function spaces

Lau

Yan²

2004

J. Aust. Math. Soc.

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“…This is quite different from the approaches in [7,8,10,11]. The proof of Theorem 1.1 depends on the Beylkin-Coifman-Rohklin wavelet decomposition of the operator 7.…”

Section: 2') S U P / (\K(xy)\ + \K(yx)\)dymentioning

confidence: 81%

Section: I(7v F)\ < T N (\\mentioning

confidence: 99%

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Wavelet decomposition of Calderón-Zygmund operators on function spaces

Lau

Yan²

2004

J. Aust. Math. Soc.

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“…If |x| > 6 √ n, we get Note that if y ∈ supp a, then 2 |θ(y)| ≤ 2 |y| ≤ 2·3 √ n < |x|, and, using the property (II N + ) of the kernel K to estimate the difference, we get In case |x − x | < 1 and |x| ≤ 10 √ n, an exact repetition of the argument on p. 85 of [3] or part (c) on p. 62 of [6] shows that …”

Section: And Each a (P )mentioning

confidence: 97%

Matrix-weighted Besov spaces

Roudenko

2002

Trans. Amer. Math. Soc.

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“…(see [17], Lemma 2.3) Let T be a Calderón-Zygmund operator satisfying T 1 = 0. Then T maps S(R n ) into L ∞ (R n ).…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

Bilinear decompositions and commutators of singular integral operators

2012

Trans. Amer. Math. Soc.

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Abstract. Let b be a BM O-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuouslyIn this paper, we find the largest subspace H 1 b (R n ) such that all commutators of Calderón-Zygmund operators are continuous fromWe also study the commutators [b, T ] for T in a class K of sublinear operators containing almost all important operators in harmonic analysis. When T is linear, we prove that there exists a bilinear operators R = R T mapping continuouslywhere S is a bounded bilinear operator fromIn the particular case of T a Calderón-Zygmund operator satisfying T 1 = T * 1 = 0 and b in BM O log (R n )-the generalized BMO type space that has been introduced by Nakai and Yabuta to characterize multipliers of BMO(R n ) -we prove that the commutatorWhen T is sublinear, we prove that there exists a bounded subbilinear operator R = R T :The bilinear decomposition (1) and the subbilinear decomposition (2) allow us to give a general overview of all known weak and strong L 1 -estimates.

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The Boundedness of Calderón-Zygmund Operators on the Spaces $\dot{F}^{\alpha, q}_p$

Cited by 58 publications

References 0 publications

Wavelet decomposition of Calderón-Zygmund operators on function spaces

Wavelet decomposition of Calderón-Zygmund operators on function spaces

Matrix-weighted Besov spaces

Bilinear decompositions and commutators of singular integral operators

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