Applying discrete Calderón’s identity, we study weighted multi-parameter mixed Hardy space . 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 of operators in mixed Journé’s class.
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...
Let μ be a nonnegative Radon measure on which satisfies μ(B(x,r)) ≤ Crⁿ for any and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition.
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . 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...
We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.
We consider the -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
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].
We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.
We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when .