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Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 676 - 689
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2017, Volume 114, Issue 1, pp. 35 - 59
We prove a multilinear local T(b) theorem that differs from previously considered multilinear local T(b) theorems in using exclusively general testing... 
42B20 (primary) | MATHEMATICS | TB-THEOREMS
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2000, Volume 101, Issue 3, pp. 499 - 513
Journal Article
Nagoya Math. J, 2006, Volume 181, pp. 41 - 62
In this paper, the authors get the L^{p} estimates for the commutators generated by strongly singular integral operators and {\rm BMO} functions and the... 
42B20
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 12/2011, Volume 21, Issue 6, pp. 1239 - 1295
We apply the Bennett–Carbery–Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We... 
Restriction | oscillatory integral operator | Mathematics | Kakeya | Analysis | 42B20 | MATHEMATICS
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2013, Volume 162, Issue 6, pp. 1203 - 1204
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2013, Volume 162, Issue 5, pp. 889 - 924
Given martingales W and Z such that W is differentially subordinate to Z , Burkholder obtained the sharp inequality E|W|^{p}\le(p^{*}-1)^{p}E|Z|^{p} , where... 
60G46 | 42A15 | 32A55 | 42B20
Journal Article
Analysis, ISSN 0174-4747, 11/2017, Volume 37, Issue 4, pp. 243 - 244
In our paper in this journal, entitled “Remarks on boundedness of Littlewood–Paley operators”, there are two incomplete statements and incompleteness in the... 
42B20 | 42B25 | Littlewood–Paley operators
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 10/2017, Volume 89, Issue 2, pp. 257 - 287
In this paper we characterize the two matrix weighted boundedness of commutators with any of the Riesz transforms (when both are matrix $$\hbox {A}_p$$ A p... 
Mathematics | Commutators | Matrix weights | Paraproducts | Analysis | 42B20
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 02/2013, Volume 162, Issue 2, pp. 417 - 434
For 1 <= p <= 2, we prove sharp weak-type (p, p)-estimates for the Beurling-Ahlfors operator acting on the radial function subspaces of L-p(C). A similar sharp... 
MARTINGALES | MATHEMATICS | CONSTANT | 60G46 | 42B20
Journal Article
The Michigan Mathematical Journal, ISSN 0026-2285, 08/2010, Volume 59, Issue 2, pp. 353 - 363
Journal Article
Osaka J. Math, 2014, Volume 51, Issue no. 1, pp. 225 - 245
In this paper we obtain the L^{p}-boundedness for the maximal functions and the singular integrals associated to surfaces (y,\phi(\lvert y\rvert)) with rough... 
42B15 | 42B20 | 42B25
Journal Article
by Liu, Yu and Wang, He
Forum Mathematicum, ISSN 0933-7741, 11/2019, Volume 31, Issue 6, pp. 1379 - 1394
In this paper, we study the Hardy type space by means of local maximal functions associated with the heat semigroup generated by , where is the generalized... 
35J10 | Riesz transform | 42B30 | Schrödinger operators | 42B20 | Hardy space
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 09/2017, Volume 115, Issue 3, pp. 545 - 598
We use the polynomial partitioning method of Guth [J. Amer. Math. Soc. 29 (2016) 371–413] to prove weighted Fourier restriction estimates in R3 with exponents... 
28A75 (secondary) | 42B20 (primary) | 42B10 | MATHEMATICS | DIMENSIONS | DISTANCE SETS | SPHERICAL AVERAGES | FOURIER-TRANSFORMS | CIRCULAR MEANS | CONJECTURE | Mathematics - Classical Analysis and ODEs
Journal Article
by Chen, P and He, DQ and Song, L
JOURNAL OF GEOMETRIC ANALYSIS, ISSN 1050-6926, 01/2019, Volume 29, Issue 1, pp. 402 - 412
We establish a weighted inequality for bilinear rough singular integrals with bound controlled by the cube of the characteristic constant of the pair of... 
MATHEMATICS | Weighted inequalities | Bilinear operators | BOUNDS | Rough singular integrals | 42B20
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 12/2019, Volume 119, Issue 6, pp. 1560 - 1597
We prove the mixed‐norm LpLq‐boundedness of a general class of singular integral operators having a multi‐parameter singularity and acting on vector‐valued... 
42B20 (primary) | Mathematics - Classical Analysis and ODEs
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 2015, Volume 15, Issue 1, pp. 165 - 208
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 06/2014, Volume 39, Issue 6, pp. 1128 - 1157
In this article we revisit the inequalities of Kato and Ponce concerning the L r norm of the Bessel potential J s  = (1 − Δ) s/2 (or Riesz potential D s  = (−... 
Primary 42B20 | Secondary 46E35 | Kato-Ponce | Fractional Leibniz rule | KORTEWEG-DEVRIES EQUATION | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | OPERATORS | EULER | Partial differential equations | Inequality | Norms | Estimates | Inequalities | Images
Journal Article
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