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Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2015, Volume 367, Issue 9, pp. 6159 - 6197
The main result of this paper is a bi-parameter T(b) is a tensor product of two pseudo-accretive functions. In the proof, we also discuss the L^2-adapted... 
MATHEMATICS | PARAPRODUCTS | PARAMETER SINGULAR-INTEGRALS | CALDERON-ZYGMUND OPERATORS | BMO
Journal Article
Publicacions Matematiques, ISSN 0214-1493, 2016, Volume 60, Issue 1, pp. 191 - 220
We show that the product BMO space can be characterized by iterated commutators of a large class of Calderon-Zygmund operators. This result follows from a new... 
Multi-parameter paraproducts | Iterated commutators | Product BMO | Dyadic shifts | multi-parameter paraproducts | MATHEMATICS | PARAPRODUCTS | HANKEL-OPERATORS | VARIABLES | product BMO | dyadic shifts | 42B20
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 10/2017, Volume 89, Issue 2, pp. 257 - 287
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00020-017-2375-9 In this... 
Commutators | Matrix weights | Paraproducts
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 08/2017, Volume 273, Issue 4, pp. 1295 - 1353
We extend the helicoidal method from [1] to the quasi-Banach context, proving in this way multiple Banach and quasi-Banach vector-valued inequalities for... 
Multi-parameter operators | Quasi-Banach spaces | Vector-valued extensions | Multilinear analysis | EXTRAPOLATION | MATHEMATICS | PARAPRODUCTS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2014, Volume 267, pp. 44 - 93
Journal Article
Advances in Mathematics, ISSN 0001-8708, 03/2016, Volume 291, pp. 24 - 58
We characterize Lp boundedness of iterated commutators of multiplication by a symbol function and tensor products of Riesz and Hilbert transforms. We obtain a... 
Multi-parameter | BMO | Iterated commutator | Journé operator | Journe operator | MATHEMATICS | HARDY-SPACES | PARAPRODUCTS | PROOF | RIESZ COMMUTATORS | OPERATORS | ITERATED COMMUTATORS
Journal Article
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 10/2017, Volume 369, Issue 10, pp. 6935 - 6951
We prove L-p estimates for a continuous version of a dyadic quadrilinear form introduced by V. Kovac (2012). This improves the range of exponents from the... 
MATHEMATICS | PARAPRODUCT
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 03/2017, Volume 272, Issue 5, pp. 2176 - 2233
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a... 
Variation norm | Iterated Fourier integral | Bilinear | Outer measure | P-VARIATION | MARTINGALES | MATHEMATICS | PARAPRODUCTS | HILBERT TRANSFORM | MULTILINEAR OPERATORS | CALDERONS CONJECTURE
Journal Article
Analysis and PDE, ISSN 2157-5045, 2016, Volume 9, Issue 5, pp. 1079 - 1113
We dominate nonintegral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators... 
Weights | Singular operators | MATHEMATICS, APPLIED | INEQUALITIES | HARDY-SPACES | HAAR MULTIPLIERS | PARAPRODUCTS | HILBERT TRANSFORM | weights | ELLIPTIC-OPERATORS | INTEGRALS | MATHEMATICS | INFINITY-FUNCTIONAL-CALCULUS | MANIFOLDS | singular operators | DOMAINS
Journal Article
INDIANA UNIVERSITY MATHEMATICS JOURNAL, ISSN 0022-2518, 2018, Volume 67, Issue 5, pp. 1711 - 1763
We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a... 
INFINITY | MATHEMATICS | RADEMACHER MAXIMAL-FUNCTION | INEQUALITIES | TENT SPACES | FOURIER MULTIPLIER THEOREMS | REPRESENTATION | PARAPRODUCTS | BOUNDEDNESS | OPERATORS | L-P-REGULARITY
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 2017, Volume 369, Issue 4, pp. 2493 - 2519
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2015, Volume 31, Issue 2, pp. 609 - 616
We prove that multilinear paraproducts are bounded from products of Lebesgue spaces L-p1 x ... x Lpm+1 to when 1 <= p(1), ... p(m), p(m+1)< infinity, 1/p(1) +... 
Paraproducts | Multilinear operators | MATHEMATICS | multilinear operators | CARLESON MEASURES
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 04/2017, Volume 262, Issue 7, pp. 3932 - 3979
In [18] Paicu and Zarnescu have studied an order tensor system which describes the flow of a liquid crystal. They have proven the existence of weak solutions,... 
Navier–Stokes | Homogeneous paraproduct | Q-Tensor | Regularity | Besov spaces | Uniqueness | SYSTEM | EXISTENCE | MATHEMATICS | Navier-Stokes
Journal Article
Annals of Probability, ISSN 0091-1798, 2019, Volume 47, Issue 2, pp. 1096 - 1135
We introduce a nonlinear paracontrolled calculus and use it to renor- malise a class of singular SPDEs including certain quasilinear variants of the periodic... 
Quasilinear SPDEs | Paraproducts | Paracontrolled distributions | ROUGH | EQUATIONS | STATISTICS & PROBABILITY | paraproducts | DRIVEN | FLOWS | paracontrolled distributions
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2016, Volume 298, pp. 581 - 611
We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators. 
Two-weight inequalities | Paraproducts | Sarason Conjecture | Toeplitz Operator | MATHEMATICS | INEQUALITIES | SPACES | HANKEL-OPERATORS | HILBERT TRANSFORM | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2018, Volume 48, Issue 2, pp. 529 - 550
In this paper, we prove that the space of two parameter matrix-valued BMO functions can be characterized by considering iterated commutators with the Hilbert... 
Commutators | BMO | Matrix-valued | Paraproducts | MATHEMATICS | matrix-valued | SPACES | commutators | DUALITY | paraproducts | HANKEL-OPERATORS | H-1
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2016, Volume 282, Issue 1, pp. 577 - 613
The boundedness of trilinear flag paraproducts from products of Hardy spaces $$H^{p} \times H^q \times H^r$$ H p × H q × H r to $$L^s$$ L s ,... 
Flag paraproducts | Littlewood–Paley theory | 42B30 | Hardy spaces | Mathematics, general | Mathematics | 42B15 | Multilinear Fourier multipliers
Journal Article
MATHEMATICAL RESEARCH LETTERS, ISSN 1073-2780, 2018, Volume 25, Issue 5, pp. 1317 - 1332
The twisted paraproduct can be viewed as a two-dimensional trilinear form which appeared in the work by Demeter and Thiele on the two-dimensional bilinear... 
MATHEMATICS | PARAPRODUCT
Journal Article
Journal des Mathematiques Pures et Appliquees, ISSN 0021-7824, 03/2012, Volume 97, Issue 3, pp. 230 - 241
In this paper, we prove that the product (in the distribution sense) of two functions, which are respectively in BMO(R{double-struck} ) and H (R{double-struck}... 
BMO multipliers | Musielak-Orlicz spaces | Hardy-Orlicz spaces | Div-curl lemma | Paraproducts | Renormalization product | Wavelet decomposition | MATHEMATICS, APPLIED | HARDY-SPACES | MATHEMATICS | DECOMPOSITIONS | div-curl lemma | BOUNDED MEAN-OSCILLATION | OPERATORS | Complex Variables | Mathematics | Analysis of PDEs | General Mathematics | Classical Analysis and ODEs
Journal Article
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