Related papers: Multi-linear operators given by singular multiplie…

In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on R^d. We are looking for uniformity with respect to parameters, which allow us to disturb the…

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.

We give a simple proof of L^p boundedness of iterated commutators of Riesz transforms and a product BMO function. We use a representation of the Riesz transforms by means of simple dyadic operators - dyadic shifts - which in turn reduces…

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r'}$-H\"ormander regularity condition. As applications, we recover a weighted estimate…

We obtain mixed $A_p$--$A_\infty$ estimates for a large family of multilinear maximal and sparse operators. Operators from this family are known to control for instance multilinear Calder\'on--Zygmund operators, square functions, fractional…

In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\'{o}n-Zygmund operators, multilinear…

We prove $L^p$ estimates for the Walsh model of the maximal bi-Carleson operator (which is a hybrid of the bilinear Hilbert transform and the Carleson maximal operator which appears naturally in the eigenfunction problem for one-dimensional…

We prove a wide range of L^p estimates for a trilinear singular integral operator motivated by dropping one average in Calder\'{o}n's second commutator. For comparison by dropping two averages in Calder\'{o}n's second commutator one faces…

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

We investigate the Hilbert transform and the maximal operator along a class of variable non-flat polynomial curves $(P(t),u(x)t)$ with measurable $u(x)$, and prove uniform $L^p$ estimates for $1<p<\infty$. In particular, via the change of…

We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-linear harmonic analysis techniques and a quantitative treatment…

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…

We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions,…

We consider a special class of the multi-linear forms studied by Brascamp and Lieb. For these forms, we are able to characterize the L^p spaces for which the form is bounded. We use this characterization to study a non-linear map that…

We prove new summability properties for multilinear operators on $\ell_p$ spaces. An important tool for this task is a better understanding of the interplay between almost summing and absolutely summing multilinear operators.

We extend to multilinear Hankel operators the fact that truncation of bounded Hankel operators is bounded. We prove and use a continuity property of a kind of bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces.

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We…