Nonsymmetric systems on nonsmooth planar domains

We study boundary value problems, in the sense of Dahlberg, for second order constant coefficient strongly elliptic systems. In this class are systems without a variational formulation, viz. the nonsymmetric systems. Various similarities and differences between this subclass and the symmetrizable systems are examined in nonsmooth domains.

     

Modulation space estimates for the fractional integral operators

We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.     

New integral mean estimates for polynomials

In this paper we prove someL ^P inequalities for polynomials, wherep is any positive number. They are related to earlier inequalities due to A Zygmund, N G De Bruijn, V V Arestov, etc. A generalization of a polynomial inequality concerning self-inversive polynomials, is also obtained.     

Weighted estimates for bilinear fractional integral operators

Moen (2016) proved weighted estimates for the bilinear fractional integrals where . We improve his results when and consider the case . As a corollary we obtain a bilinear Stein–Weiss inequality where .     

On area integral estimates for solutions to parabolic systems in time-varying and non-smooth cylinders

In this paper we prove results relating the (parabolic) non-tangential maximum operator and appropriate square functions in for solutions to general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylinders . In particular we prove a global as well as a local and scale invariant equivalence between the parabolic non-tangential maximal operator and appropriate square functions for solutions of our system. The novelty of our approach is that it is not based on singular integrals, the prevailing tool in the analysis of systems in non-smooth domains. Instead the methods explored have recently proved useful in the analysis of elliptic measure associated to non-symmetric operators through the work of Kenig-Koch-Pipher-Toro and in the analysis of caloric measure without the use of layer potentials.

     

Modular estimates of fractional integral operators and k-plane transforms

The modular estimates for the fractional integral operators and the k-plane transforms are obtained in this paper. These estimates are obtained by using the modular estimates of Hardy operators and the modular interpolation theorem.     

Linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces

We obtain bilinear estimates for oscillatory integral operators which are variable coefficient generalizations of bilinear restriction estimates for hypersurfaces. As applications, we improve the known estimates for oscillatory integrals.     

Sharp norm estimates for a class of integral operators

ABSTRACT

Norm comparison inequalities for two integral operators with radial kernels are established. Sharp norm estimates for operators with monotone and convex/concave kernels are obtained. Integral analogues of Bennett's estimates for summability matrices are given. The exact operator norms with power weights are also obtained for a class of integral operators with radial quasimonotone kernels.     

Weighted estimates for singular integral operators and commutators associated with the sections

In this paper we prove weighted estimates for singular integral operators and commutators associated with the sections.     

Some BMO estimates for vector-valued multilinear singular integral operators

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

Weak estimates for commutators of fractional integral operators

By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function, the weak type LlogL estimates for the commutators of the fractional integral operator and the related maximal operator are established.     

Weighted estimates for commutators of one-sided oscillatory integral operators

In this paper, we study the weighted norm inequalities for commutators formed by a class of one-sided oscillatory integral operators and functions in one-sided BMO spaces.     

Endpoint estimates for commutators of multilinear fractional integral operators

In this paper, the weak type LlogL estimate for the multilinear fractional commutator is obtained by introducing a new kind of maximal operator of the multilinear fractional order associated with the mean Luxumburg norm and using the technique of sharp function.     

一类奇异积分算子的加权估计

假设A是一个Young函数,MD#为广义sharp极大函数.本文首先引进了LA-Hrmander条件,对于满足LA-Hrmander条件的算子T,得到了与T相关的广义sharp极大函数的估计.然后,再利用该估计得到了算子T的加权Lp范数被Hardy-Littlewood极大函数和与Aˉ相关的极大函数的加权Lp范数所控制(0相似文献   

Lack of natural weighted estimates for some singular integral operators

We show that the classical Hörmander condition, or analogously the -Hörmander condition, for singular integral operators is not sufficient to derive Coifman's inequality

where , is the Hardy-Littlewood maximal operator, is any weight and is a constant depending upon and the constant of . This estimate is well known to hold when is a Calderón-Zygmund operator.

As a consequence we deduce that the following estimate does not hold:

where and where is an arbitrary weight. However, by a recent result due to A. Lerner, this inequality is satisfied whenever is a Calderón-Zygmund operator.

One of the main ingredients of the proof is a very general extrapolation theorem for weights.

     

Pointwise estimates for the maximal multilinear singular integral operators

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) estimate for the maximal multilinear singular integral operators.     

Weighted estimates for commutators of singular integral operators with non-doubling measures

Letμbe a nonnegative Radon measure on R~d which only satisfiesμ(B(x,r))≤C_0r~n for all x∈R~d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.     

Square area integral estimates for subharmonic functions in NTA domains

In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic functionu in a bounded NTA domainD inR ⁿ . We achieve this by showing that a weighted Riesz measure ofu is a Carleson measure, with the Carleson norm bounded by a constant independent ofu. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions inD.     

Square area integral estimates for subharmonic functions in NTA domains

In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic functionu in a bounded NTA domainD inR ⁿ . We achieve this by showing that a weighted Riesz measure ofu is a Carleson measure, with the Carleson norm bounded by a constant independent ofu. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions inD.