| 1. |
- Aleman, Alexandru, et al.
(författare)
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Characterizations of a limiting class B∞ of Békollé–Bonami weights
- 2019
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230. ; 35:6, s. 1677-1692
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Tidskriftsartikel (refereegranskat)abstract
- We explore properties of the class of Békollé–Bonami weights B∞ introduced by the authors in a previous work. Although Békollé–Bonami weights are known to be ill-behaved because they do not satisfy a reverse Hölder property, we prove that when restricting to a class of weights that are “nearly constant on top halves”, one recovers some of the classical properties of Muckenhoupt weights. We also provide an application of this result to the study of the spectra of certain integral operators.
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| 2. |
- Aleman, Alexandru, et al.
(författare)
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Sarason conjecture on the Bergman space
- 2017
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Ingår i: International Mathematics Research Notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2017:14, s. 4320-4349
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Tidskriftsartikel (refereegranskat)abstract
- We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present some results about two-weighted estimates for the Bergman projection. Finally, we introduce the class B∞ and give sharp estimates for the one-weighted Bergman projection.
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| 3. |
- 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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| 4. |
- 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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| 5. |
- Gorkin, Pamela, et al.
(författare)
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Thin sequences and the Gram matrix
- 2014
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Ingår i: Archiv der Mathematik. - : Springer Science and Business Media LLC. - 0003-889X .- 1420-8938. ; 103:1, s. 93-99
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Tidskriftsartikel (refereegranskat)abstract
- We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 <= p <= infinity.
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| 6. |
- Gorkin, Pamela, et al.
(författare)
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Thin sequences and their role in H-p theory, model spaces, and uniform algebras
- 2015
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Ingår i: Revista Matemática Iberoamericana. - 2235-0616. ; 31:3, s. 841-864
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we revisit some facts about thin interpolating sequences in the unit disc from three perspectives: uniform algebras, model spaces, and H-p spaces. We extend the notion of asymptotic interpolation to H-p spaces, for 1 <= p <= infinity, providing several new ways to think about these sequences.
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| 7. |
- 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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| 8. |
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| 9. |
- Jacob, Birgit, et al.
(författare)
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Applications of Laplace–Carleson embeddings to admissibility and controllability
- 2014
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 52:2, s. 1299-1313
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Tidskriftsartikel (refereegranskat)abstract
- It is shown how results on Carleson embeddings induced by the Laplace transform can be used to derive new and more general results concerning the weighted (infinite-time) admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. As an example, the heat equation is considered. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterized by means of a new result about weighted interpolation.
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| 10. |
- Jacob, Birgit, et al.
(författare)
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On Laplace-Carleson embedding theorems
- 2013
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 264:3, s. 783-814
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Tidskriftsartikel (refereegranskat)abstract
- This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure or a measure supported on a strip, and complete necessary and sufficient conditions for a bounded embedding are given in many cases. (C) 2012 Elsevier Inc. All rights reserved.
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