arXiv subjects

Wendolín Damián

Publications and source records attributed to Wendolín Damián.

6 recordsLinked to original sources

arXiv2016

New bounds for bilinear Calderón-Zygmund operators and applications

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 $A_{\infty}$ 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.

math.CA↗

arXiv2014

Calderón-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities

The recent proof of the sharp weighted bound for Calderón-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different $A_p$ weight constants. The reason why these are sought after is that the product will be strictly smaller than the original one-constant bound. We prove a variety of these bounds in spaces of homogeneous type, using the new techniques of Lerner, for both operators and commutators.

math.CA↗

arXiv2013

Compact bilinear commutators: the weighted case

Commutators of bilinear Calderón-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact on appropriate products of weighted Lebesgue spaces.

math.CA↗

arXiv2013

Compactness properties of commutators of bilinear fractional integrals

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.

math.CA↗

arXiv2013

Weighted estimates for the multilinear maximal function

A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows to obtain a multilinear analogue of Sawyer's two weight theorem for the multisublinear maximal function \mathcal{M} introduced in Lerner et al. A multilinear version of the B_p theorem from Hytönen and Pérez is also obtained and a mixed A_{\vec{P}}-W_{\vec{P}}^{\infty} bound for \mathcal{M} is proved as well.

math.CA↗

arXiv2012

Sharp weighted bounds for multilinear maximal functions and Calderón-Zygmund operators

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $\Mm$ introduced in \cite{LOPTT} and for multilinear Calderón-Zygmund operators. In particular we obtain a sharp mixed "$A_p-A_{\infty}$" bound for $\Mm$, some partial results related to a Buckley-type estimate for $\Mm$, and a sufficient condition for the boundedness of $\Mm$ between weighted $L^p$ spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón-Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work. Then we obtain a multilinear version of the "$A_2$ conjecture". Several open problems are posed.

math.CA↗