Abstract
In this paper, the authors introduce weak martingale Hardy-type spaces associated with a quasi-Banach function lattice. The authors then establish the atomic characterizations of these weak martingale Hardy-type spaces. As applications, the authors give the sufficient conditions for the boundedness of σ-sublinear operators from weak martingale Hardy-type spaces to a quasi-Banach function lattice. Furthermore, the authors clarify the relation among different weak martingale Hardy-type spaces in the framework of a rearrangement-invariant quasi-Banach function space. Finally, the authors apply these results to the weighted Lorentz space and the generalized grand Lebesgue space.
Funding source: China Postdoctoral Science Foundation
Award Identifier / Grant number: 2019M662797
Funding statement: This project is supported by China Postdoctoral Science Foundation (Grant No. 2019M662797).
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the variance of the nodal volume of arithmetic random waves
- On length densities
- On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
- Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
- On cutting blocking sets and their codes
- Inertia groups and smooth structures on quaternionic projective spaces
- On the number of zeros of diagonal quartic forms over finite fields
- Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
- A dual version of Huppert's ρ-σ conjecture for character codegrees
- A topological correspondence between partial actions of groups and inverse semigroup actions
- On homotopy braids
- Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
- The Shintani double zeta functions
- Homological dimensions relative to preresolving subcategories II
- Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
- A converse theorem for quasimodular forms
Articles in the same Issue
- Frontmatter
- On the variance of the nodal volume of arithmetic random waves
- On length densities
- On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
- Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
- On cutting blocking sets and their codes
- Inertia groups and smooth structures on quaternionic projective spaces
- On the number of zeros of diagonal quartic forms over finite fields
- Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
- A dual version of Huppert's ρ-σ conjecture for character codegrees
- A topological correspondence between partial actions of groups and inverse semigroup actions
- On homotopy braids
- Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
- The Shintani double zeta functions
- Homological dimensions relative to preresolving subcategories II
- Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
- A converse theorem for quasimodular forms