| 1. |
- Bui, Anh, et al.
(författare)
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Weighted bounds for multilinear operators with non-smooth kernels
- 2015
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds {for} certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$ and these results are new in the literature
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| 2. |
- Bui, T. A., et al.
(författare)
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A note on weighted bounds for singular operators with nonsmooth kernels
- 2017
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 236:3, s. 245-269
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Tidskriftsartikel (refereegranskat)abstract
- Let T be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on R-n. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual Holder continuity of kernels of multilinear Calderon-Zygmund singular integral operators. In this paper, given a suitable multiple weight w, we obtain a bound for the weighted norm of T in terms of w. As applications, we obtain new weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schrodinger operators on R-n.
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| 3. |
- Bui, T. A., et al.
(författare)
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Weighted Bounds for Multilinear Square Functions
- 2017
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Ingår i: Potential Analysis. - : Springer Science and Business Media LLC. - 0926-2601 .- 1572-929X. ; 46:1, s. 135-148
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Tidskriftsartikel (refereegranskat)abstract
- Let with 1 < p (1), aEuro broken vertical bar, p (m) < a, 1/p (1)+a+1/p (m) =1/p and . In this paper, we investigate the weighted bounds with dependence on aperture alpha for multilinear square functions . We show that. This result extends the result in the linear case which was obtained by Lerner in 2014. Our proof is based on the local mean oscillation technique presented firstly to find the weighted bounds for Caldern-Zygmund operators. This method helps us avoiding intrinsic square functions in the proof of our main result.
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| 4. |
- Damián, Wendolín, et al.
(författare)
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New bounds for bilinear Calderon-Zygmund operators and applications
- 2018
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230. ; 34, s. 1177-1210
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Tidskriftsartikel (refereegranskat)abstract
- © European Mathematical Society. In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderón-Zygmund operators with Dini-continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple A∞ constants inspired in the Fujii-Wilson and Hrusčěv classical constants. These estimates have many new applications including mixed bounds for multilinear Calderón-Zygmund operators and their commutators with BMO functions, square functions and multilinear Fourier multipliers.
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| 5. |
- Damian, Wendolin, et al.
(författare)
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New bounds for bilinear Calderon-Zygmund operators and applications
- 2018
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Ingår i: Revista Matematica Iberoamericana. - : European Mathematical Society - EMS - Publishing House GmbH. - 0213-2230 .- 2235-0616. ; 34:3, s. 1177-1210
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Tidskriftsartikel (refereegranskat)abstract
- In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderon-Zygmund operators with Dini-continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytonen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple A(infinity), constants inspired in the Fujii-Wilson and Hruscev classical constants. These estimates have many new applications including mixed bounds for multilinear Calderon-Zygmund operators and their commutators with BMO functions, square functions and multilinear Fourier multipliers.
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| 6. |
- Goodarzi, M. M., et al.
(författare)
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Relations between Schramm spaces and generalized Wiener classes
- 2017
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 450:1, s. 829-838
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Tidskriftsartikel (refereegranskat)abstract
- We give necessary and sufficient conditions for the embeddings ABV((p)) subset of Gamma BV(qn up arrow q) and Phi BV subset of BV(qn up arrow q). As a consequence, a number of results in the literature, including a fundamental theorem of Perlman and Waterman, are simultaneously extended. (C) 2017 Elsevier Inc. All rights reserved.
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| 7. |
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| 8. |
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| 9. |
- Hormozi, Mahdi, 1980
(författare)
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Inclusion of Lambda BV(p) spaces in the classes H-omega(q)
- 2013
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 404:2, s. 195-200
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Tidskriftsartikel (refereegranskat)abstract
- A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. This corrects and extends an earlier result of a paper from 2005.
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| 10. |
- Hormozi, Mahdi, 1980, et al.
(författare)
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Inclusions of Waterman-Shiba spaces into generalized Wiener classes
- 2014
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 419:1, s. 428-432
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Tidskriftsartikel (refereegranskat)abstract
- The characterization of the inclusion of Waterman-Shiba spaces Lambda BV(p) into generalized Wiener classes of functions BV (q; delta) is given. It uses a new and shorter proof and extends an earlier result of U. Goginava.
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