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Weighted multi-parameter mixed Hardy spaces and their applications

Wei Ding, Yun Xu, Yueping Zhu (2022)

Czechoslovak Mathematical Journal

Applying discrete Calderón’s identity, we study weighted multi-parameter mixed Hardy space H mix p ( ω , ℝ n 1 × ℝ n 2 ) . Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on H mix p ( ω , ℝ n 1 × ℝ n 2 ) of operators in mixed Journé’s class.

Weighted norm inequalities for Calderón-Zygmund operators without doubling conditions.

Xavier Tolsa (2007)

Publicacions Matemàtiques

Let µ be a Borel measure on Rd which may be non doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Crn for all x ∈ Rd, r > 0 and for some fixed n with 0 < n ≤ d. In this paper we introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if µ(B(x, r)) ≈ rn for x ∈ supp(µ), and we show that all n-dimensional Calderón-Zygmund operators are bounded on Lp(w dµ) if and only if N is bounded on Lp(w dµ), for a fixed p ∈ (1, ∞). Also, we prove...

Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu, Dachun Yang (2008)

Studia Mathematica

Let μ be a nonnegative Radon measure on ℝ d which satisfies μ(B(x,r)) ≤ Crⁿ for any x ∈ ℝ d and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with A p ϱ ( μ ) weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with A ∞ ϱ ( μ ) weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Sergio Antonio Tozoni (2004)

Studia Mathematica

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis ( e j ) j ≥ 1 . Given an operator T from L c ∞ ( X ) to L¹(X), we consider the vector-valued extension T̃ of T given by T ̃ ( ∑ j f j e j ) = ∑ j T ( f j ) e j . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...

What is van der Corput's lemma in higher dimensions?

Anthony Carbery, James Wright (2002)

Publicacions Matemàtiques

We consider variants of van der Corput's lemma in higher dimensions.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals

Carlos E. Kenig, Wolfgang Staubach (2007)

Studia Mathematica

We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their L p boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.

ω-Calderón-Zygmund operators

Sijue Wu (1995)

Studia Mathematica

We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when ω ∈ A ∞ .

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