Four Lectures on Real Hp Spaces

Lu, Shanzhen

doi:10.1142/9789812831194

Cited by 71 publications

(82 citation statements)

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“…of the classical δ-type Calderón-Zygmund operator, respectively, from H p (R n ) to H p (R n ) and from H p (R n ) to L p (R n ) for δ ∈ (0, 1] and p ∈ ( n n+δ , 1], which is a well-known result (see, for example, [5,65,49]). …”

Section: ])mentioning

confidence: 74%

Anisotropic Hardy-Lorentz spaces and their applications

Yang

Yuan

2016

Sci. China Math.

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Let p ∈ (0, 1], q ∈ (0, ∞] and A be a general expansive matrix on R n . The authors introduce the anisotropic Hardy-Lorentz space H p,q A (R n ) associated with A via the non-tangential grand maximal function and then establish its various realvariable characterizations in terms of the atomic or the molecular decompositions, the radial or the non-tangential maximal functions, or the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on R n . As applications, the authors firstA (R n ) and H p2,q2A (R n ) with 0 < p 1 < p < p 2 < ∞ and q 1 , q, q 2 ∈ (0, ∞], and also between H p,q1A (R n ) andA (R n ) with p ∈ (0, ∞) and 0 < q 1 < q < q 2 ≤ ∞ in the real method of interpolation. The authors then establish a criterion on the boundedness of sublinear operators from H p,q A (R n ) into a quasi-Banach space; moreover, the authors obtain the boundedness of δ-type Calderón-Zygmund operators from, 1] and q ∈ (0, ∞], as well as the boundedness of some Calderón-Zygmund operators from H p,q A (R n ) to L p,∞ (R n ), where b := | det A|, λ − := min{|λ| : λ ∈ σ(A)} and σ(A) denotes the set of all eigenvalues of A.

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Section: ])mentioning

confidence: 74%

Anisotropic Hardy-Lorentz spaces and their applications

Yang

Yuan

2016

Sci. China Math.

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“…[8], [24] Let 1 ≤ p < ∞, b ∈ BMO(R n ). Then for any ball B ⊂ R n , the following statements are true (1) There exist constants C 1 , C 2 such that for all α > 0…”

Section: Weighted Estimates For the Commutatorsmentioning

confidence: 99%

Boundedness of oscillatory integral operators and their commu- tators on weighted Morrey spaces

Shi¹,

Fu²,

Lu³

2013

Sci. Sin.-Math.

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“…It is well known that the classical Hardy spaces were the dual spaces of BMO spaces and were the natural alternative for Lebesgue spaces when p < 1. For some classical work on classical Hardy spaces, we refer to [6], [8], [9], [14] and [19]. In [36], Rosa and Segovia introduced the one-sided Hardy space H q + (0 < q ≤ 1).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Some one-sided estimates for oscillatory singular integrals

Pan

et al. 2014

Nonlinear Analysis: Theory, Methods & Applications

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Abstract. The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces H 1 + (w) is proved. It is here also show that the H 1 + (w) theory of oscillatory singular integrals above cannot be extended to the case of H q + (w) when 0 < q < 1 and w ∈ A + p , a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted L p -boundednesss of the oscillatory singular integral is given.

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Four Lectures on Real Hp Spaces

Cited by 71 publications

References 0 publications

Anisotropic Hardy-Lorentz spaces and their applications

Anisotropic Hardy-Lorentz spaces and their applications

Boundedness of oscillatory integral operators and their commu- tators on weighted Morrey spaces

Some one-sided estimates for oscillatory singular integrals

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