Variable weak Hardy spaces and their applications

By Xianjie Yan, Dachun Yang, Wen Yuan, Ciqiang Zhuo. 2016

109 citations recorded by the source corpus.

Abstract Let p ( ⋅ ) : R n → ( 0 , ∞ ) be a variable exponent function satisfying the globally log-Holder continuous condition. In this article, the authors first introduce the variable weak Hardy space on R n , WH p ( ⋅ ) ( R n ) , via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain various equivalent characterizations of WH p ( ⋅ ) ( R n ) , respectively, by means of atoms, molecules, the Lusin area function, the Littlewood–Paley g-function or g λ ⁎ -function. As an application, the authors establish the boundedness of convolutional δ-type and non-convolutional γ-order Calderon–Zygmund operators from H p ( ⋅ ) ( R n ) to WH p ( ⋅ ) ( R n ) including the critical case when p − = n / ( n + δ ) or when p − = n / ( n + γ ) , where p − : = ess inf x ∈ R n p ( x ) .

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/7f8c62419d85bc48e97549bf988e838162754fe9

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Songbai Wang
5. Jun Liu
6. Yong Jiao
7. Dejian Zhou
8. Lian Wu

Citations in the corpus

• Real-variable characterizations of Orlicz-slice Hardy spaces (2018, methodology): “We recall the notion of β-order Calderón-Zygmund operators as follows (see, for example, [45]).”
• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, background): “Particularly, our assumptions on the Littlewood–Paley functions are much weaker than the corresponding assumptions in [67, 52, 74] (see Remark 3.”
• Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, methodology): “[78] first introduced the variable weak Hardy spaces on R and established various real-variable characterizations of these spaces; as application, the boundedness of some Calderón-Zygmund operators in the critical case was also presented.”
• Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, methodology): “It is proved in [53] that for any b ∈ ( 0,min { n n+s+1 , q }) , q1 ∈ ( n [n+s+1]b , 1 b ) and a ∈ ( 0, 1 − 1 q1 ) ,”