Boundedness of the twisted paraproduct [PDF]
Rev. Mat. Iberoam. 28 (2012), no. 4, 1143-1164, 2010 We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].
arxiv +1 more source
Endpoint Estimates for N-dimensional Hardy Operators and Their Commutators [PDF]
Sci China Math 2012, 2011 In this paper, it is proved that the higher dimensional Hardy operator is bounded from Hardy space to Lebesgue space. The endpoint estimate for the commutator generated by Hardy operator and (central) BMO function is also discussed.
arxiv +1 more source
A T(L) theorem for the Calderón--Zygmund operators in BMO($\mathbb{R}^d$) [PDF]
arXiv, 2023 A variant of the global $T(1)$ criterion to characterize the bounded Calder\'{o}n--Zygmund operators on BMO($\mathbb{R}^d$) is proved. We apply it to the certain Calder\'on commutators.
arxiv
Multiple Hilbert transform associated with polynomials [PDF]
arXiv, 2013 We study conditions determining the $L^p$ boundedness of multiple Hilbert transforms associated with polynomials.
arxiv
Fourier multipliers for non-symmetric Lévy processes [PDF]
arXiv, 2010 We study Fourier multipliers resulting from martingale transforms of general L\'evy processes.
arxiv
Variational truncations of singular integrals on spaces of homogeneous type [PDF]
arXiv, 2020 We prove sharp weighted estimates for $r$-variations of averages and truncated singular integrals on suitable spaces of homogeneous type, including homogeneous nilpotent Lie groups.
arxiv
Weighted Weak (1,1) estimates for one-sided oscillatory singular integrals [PDF]
arXiv, 2011 We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory singular integrals with smooth kernel.
arxiv
Weighted Norm Inequalities for One-sided Oscillatory Integral Operators [PDF]
arXiv, 2011 The purpose of this paper is to establish the weighted norm inequalities of one-sided oscillatory integral operators by the aid of interpolation of operators with change of measures.
arxiv
Weighted norm inequalities for fractional oscillatory integrals and applications [PDF]
arXiv, 2011 We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.
arxiv
Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces [PDF]
arXiv, 2011 It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
arxiv