| 1. |
- Bakas, Odysseas, et al.
(författare)
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Notes on Hlog : structural properties, dyadic variants, and bilinear H1-BMO mappings
- 2022
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Ingår i: Arkiv för matematik. - 0004-2080 .- 1871-2487. ; 60:2, s. 231-275
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Tidskriftsartikel (refereegranskat)abstract
- This article is devoted to a study of the Hardy space Hlog(Rd) introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space H1 and a function in BMO to distributions that belong to Hlog based on dyadic paraproducts. We also point out analogues of classical results of Hardy–Littlewood, Zygmund, and Stein for Hlog and related Musielak–Orlicz spaces.
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| 2. |
- Cruz-Uribe, David, et al.
(författare)
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Weak endpoint bounds for matrix weights
- 2021
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230. ; 37:4, s. 1513-1538
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Tidskriftsartikel (refereegranskat)abstract
- We prove quantitative, matrix weighted, endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderon-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class A1 introduced by M. Frazier and S. Roudenko. Even in the scalar case, our estimates are sharper than the results implicit in the literature.
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| 3. |
- Isralowitz, Joshua, et al.
(författare)
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Commutators in the two scalar and matrix weighted setting
- 2022
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 106:1, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of research initiated by the first two authors.
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| 4. |
- Partington, Jonathan R., et al.
(författare)
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Laplace–Carleson Embeddings on Model Spaces and Boundedness of Truncated Hankel and Toeplitz Operators
- 2020
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 92:4
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Tidskriftsartikel (refereegranskat)abstract
- A characterisation is given of bounded embeddings from weighted L2 spaces on bounded intervals into L2 spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen spaces). As an application necessary and sufficient conditions are given for the boundedness of truncated Hankel and Toeplitz integral operators, including the weighted case, and on model spaces.
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