Weighted estimates for the multisublinear maximal function

A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows obtaining a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function $\mathcal{M }$ introduced by Lerner et al. (Adv Math 220:1222–1264, 2009). A multilinear version of the $B_p$ theorem from Hytönen and Pérez (Anal PDE, 2013) is also obtained and a mixed $A_{\overrightarrow{ P}}-W_{\overrightarrow{ P}}^{\infty }$ bound for $\mathcal{M }$ is proved as well.     

Weighted estimates for stationary Navier-Stokes equations

We show Morrey-type estimates for the weak solution of the periodic Navier-Stokes equations in dimensionN, 5 <N < 10. ForN < 8, we prove the existence of a maximum solution.     

Weighted estimates for multilinear pseudodifferential operators

In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.     

Weighted estimates for conic Fourier multipliers

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on \(L^p(\mathbb {R}^3)\) with \(1 .     

Weighted estimates for parametrized Littlewood-Paley operators

In this paper, we obtain some boundedness on the weighted Lebesgue spaces and the weighted Hardy spaces for the parametrized Littlewood-Paley operators with the kernel Ω satisfying the logarithmic type Lipschitz conditions.     

向量值极大积分交换子的加权估计

考虑了极大向量值交换子的加权有界性.分别得到了强型和弱型的加权模不等式,其中权函数是非负局部可积函数.     

Weighted estimates for maximal multilinear commutators

Let T be a Calderón–Zygmund operator with regular kernel K and T * _b be the maximal multilinear commutator defined by . In this paper, the following weighted estimates for T * _b are discussed. Precisely, for 0 < p < ∞, ω ∈ A _∞ and b _j ∈ Osc equation/tex2gif-inf-5.gif, r_j ≥ 1, j = 1, … , m , there exists a positive constant C such that . For p = 1 and ω ∈ A ₁, the weighted weak L (log L )^1/r ‐type estimates are also established. Our theorems are parallel to the ones of the multilinear commutators of Calderón–Zygmund operators obtained in [18] and extend the main result in [14] essentially. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weighted estimates for the Hilbert transform of odd functions

The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak, or extra-weak type estimates in Orlicz classes for the integral operator $$H_0 f(x) = \frac{2}{\pi }\int_0^\infty {\frac{{yf(y)}}{{x^2 - y^2 }}dy, x \in (0,\infty )}$$ .     

Weighted estimates for the multilinear commutators of the Littlewood-Paley operators

In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.     

Weighted estimates for rough oscillatory singular integrals

Weighted L^p estimates (1<p<∞) are shown for oscillatory singular integral operators with polynomial phase and a rough kernel of the form e^iP(x,y)Ω(x−y)h(|x−y|)|x−y|⁻ⁿ. We assume that Ω∈L logL(Sⁿ⁻¹) is homogeneous of degree zero and ∫_Sn-1Ω=0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the A_p condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω.     

Weighted minimal contrast estimates and simulation problems

While complex systems are being designed, a number of statistical experiments are carried out. The present paper is devoted to the development of methods of correlated processes which increase the efficiency of statistical tests by designing dependent experiments and simultaneous processing of the obtained data. The deficiency of the usual approaches in this field consists in their specialization in complex systems modelled by functionals of the mathematical expectaition only. We consider here the technique of minimal contrast estimation which allows us to extend the methods of correlated processes to a large family of functionals. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 150–163, Perm, 1990.     

Weighted Schauder estimates for Evolution Stokes Problem

Abstract We prove the solvability of the evolution Stokes problem in bounded or exterior domain Ω∈ Rⁿ under the assumption that the initial value of the velocity vector field v₀ belongs to C^s(Ω), (in particular, it can be only continuous). The solution is obtained in some weighted H?lder spaces. This result makes it possible to prove the local solvability of a nonlinear problem under the same assumption concerning v₀. Keywords: Stokes equations, Weighted norms Mathematics Subject Classification (2000): 35Q30, 76D03     

Weighted estimates for the incompressible fluid in exterior domains

For a strong solution u(x,t) of the Navier-Stokes equations in exterior domain Ω in Rn where n=2,3, we study the time decay of ‖α|x|u(t)Lp_‖ for α<n. When a domain has a boundary, pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary. To overcome the difficulty, we adopt the ideas in [H.-O. Bae, B.J. Jin, Temporal and spatial decay rates of Navier-Stokes solutions in exterior domains, Bull. Korean Math. Soc. 44 (3) (2007) 547-567; H.-O. Bae, B.J. Jin, Asymptotic behavior for the Navier-Stokes solutions in 2D exterior domains, J. Funct. Anal. 240 (2006) 508-529] and we will extend Bae and Jin's results by modifying their methods.     

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 uncertainty bounds and growth estimates for fractional fourier transforms

Gelfand–Shilov spaces are spaces of entire functions defined in terms of a rate of growth in one direction and a concomitant rate of decay in an orthogonal direction. Gelfand and Shilov proved that the Fourier transform is an isomorphism among certain of these spaces. In this article we consider mapping properties of fractional Fourier transforms on Gelfand–Shilov spaces. Just as the Fourier transform corresponds to rotation through a right angle in the phase plane, fractional Fourier transforms correspond to rotations through intermediate angles. Therefore, the aim of fractional Fourier estimates is to set up a correspondence between growth properties in the complex plane versus decay properties in phase space.     

Weighted weak type estimates for commutators of the Marcinkiewicz integrals

In this paper the authors give the weighted weak L logL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed.     

Weighted endpoint estimates for commutators of Marcinkiewicz integrals

Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.     

Weighted estimates of singular integrals and their applications

We give a survey of research on the problem of single-weighted and double-weighted estimates of strong and weak types for the Hardy-Littlewood maximal function, Riesz potentials, singular integral operators, and harmonic functions. Necessary and sufficient conditions on the weight are given under which weighted estimates are valid (Muckenhoupt's A_p-condition, Sawyer's condition, etc.). Special attention is given to papers which appeared after 1980 and the latest results, published as reports and preprints.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 21, pp. 42–129, 1983.