Displaying similar documents to “A weak molecule condition for certain Triebel-Lizorkin spaces”

Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces

Wenchang Li, Jingshi Xu (2017)

Czechoslovak Mathematical Journal

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Recently, the weak Triebel-Lizorkin space was introduced by Grafakos and He, which includes the standard Triebel-Lizorkin space as a subset. The latter has a wide applications in aspects of analysis. In this paper, the authors firstly give equivalent quasi-norms of weak Triebel-Lizorkin spaces in terms of Peetre's maximal functions. As an application of those equivalent quasi-norms, an atomic decomposition of weak Triebel-Lizorkin spaces is given.

Para-accretive functions, the weak boundedness property and the Tb theorem.

Yongsheng Han, Eric T. Sawyer (1990)

Revista Matemática Iberoamericana

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G. David, J.-L. Journé and S. Semmes have shown that if b and b are para-accretive functions on R, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L if and only if Tb ∈ BMO, T*b ∈ BMO and MTM has the weak boundedness property. Conversely they showed that when b = b = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b and b is necessary for the Tb Theorem to hold in general. In addition,...

The Cauchy problem for the magneto-hydrodynamic system

Marco Cannone, Changxing Miao, Nicolas Prioux, Baoquan Yuan (2006)

Banach Center Publications

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We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method. ...

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

Non-negative solutions to fast diffusions.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1988)

Revista Matemática Iberoamericana

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The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation ∂u/∂t = ∆φ(u),   x ∈ Rn, 0 < t < T ≤ +∞.

Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics

Nobu-Yuki Suzuki (2017)

Bulletin of the Section of Logic

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We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the Z-normality, which is a weak variant of the disjunction property. These weak variants were presented in the author’s previous paper [16]. In the present paper, the Kripke sheaf semantics is used.

Calderón-type reproducing formula and the Tb theorem.

Yong Sheng Han (1994)

Revista Matemática Iberoamericana

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In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.