相关论文: Weighted estimates for multilinear Fourier multipl…
In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators $T_b^m$. Our results are new even for the first order commutator $T_b^1$. A new bump type…
This 1995 paper contains a sharp version of the classical Marcinkiewicz multiplier theorem for the class of homogeneous Fourier multipliers in two dimensions; here a one-dimensional Marcinkiewicz condition is sufficient. Examples are given…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
This note is devoted to establishing two-weight estimates for commutators of singular integrals. We combine multilinearity with product spaces. A new type of two-weight extrapolation result is used to yield the quasi-Banach range of…
In this paper, we extend the C\'ordoba-Fefferman square function estimate for the parabola to a weighted setting. Our weighted square function estimate is derived from a weighted wave envelope estimate for the parabola. The bounds are…
We introduce multilinear analogues of dyadic paraproduct operators and Haar Multipliers, and study boundedness properties of these operators and their commutators. We also characterize dyadic BMO functions via the boundedness of certain…
We introduce a weighted quasisymmetric enumerator function associated to generalized permutohedra. It refines the Billera, Jia and Reiner quasisymmetric function which also includes the Stanley chromatic symmetric function. Beside that it…
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 transform. Specifically, we prove that $$\| B \|_{BMO} \lesssim \| [[M_B,…
Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to…
We prove the off-diagonal estimates of the bilinear iterated commutators in the two-weight setting. The upper bound is established via sparse domination, and the lower bound is proved by the median method. Our methods are so flexible so…
We obtain weighted mixed inequalities for the first order commutator of singular integral operators in the Schr\"odinger setting. Concretely, for $0<\delta\leq 1$ we give estimates of commutators of Schr\"odinger-Calder\'on-Zygmund…
In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation…
Bilinear Fourier multipliers of the form $e^{i (|\xi| + |\eta|+ |\xi + \eta|)} \sigma (\xi, \eta)$ are considered. It is proved that if $\sigma (\xi, \eta)$ is in the H\"ormander class $S^{m}_{1,0} (\mathbb{R}^{2n})$ with $m=-(n+1)/2$ then…
We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient…
We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb{R}^n)$ with Gaussian kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n$. Assume that $\vec{b}=(b_1,b_2,\cdots,b_m)$ is a…
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.
Analogues of multi-paramter multiplier operators on R^d are defined on the torus T^d. It is shown that these operators satisfy the classical Coifman-Meyer theorem. In addition, L log L and L (log L)^n end-point estimates are proved.
We introduce a weighted version of the pluripotential theory on complex K\"{a}hler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its…
In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple…