首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 109 毫秒
1.
A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted L^p1(Rn)×···×L^pm(Rn) with weight MBw for certain maximal operator MB and general weight w, and a two-weight weighted norm estimate for this operator, are obtained.  相似文献   

2.
In this paper, we obtain certain Lpw(Rn)-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ (n-1)/2, b ∈ BMO(Rn), 1 p ∞ and w ∈ A1 . Moreover, if δ (n-1)/2, then we prove that the above maximal operator admits weak type (H1w(Rn), L1w(Rn))-mapping properties for b ∈ BMO(Rn) and w ∈ A1 under the surface condition on Σed .  相似文献   

3.
By using Fourier multiplier theorems, the maximal B-regularity of ordinary integro-differential operator equations is investigated. It is shown that the corresponding differential operator is positive and satisfies coercive estimate. Moreover, these results are used to establish maximal regularity for infinite systems of integro-differential equations.  相似文献   

4.
In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator M~kf,certain equivalence between M~kf andthe Zygmund class LLog~aL are established on R~n,so that we generalizeStein's LLogL theorem.In Section 3,a simple induction enables us toprove such extensions on K~n,the n-dimensional linear space over a localfield K,without recoursing to Leckband's result.  相似文献   

5.
In this paper, we consider the local and global solution for the nonlinear Schrodinger equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from the Strichartz type estimate, Kato's smoothing effect and the maximal function (in time) estimate for the free SchrSdinger operator.  相似文献   

6.
For a function?satisfying some suitable growth conditions,consider the following general dispersive equation defined by■where■is a pseudo-differential operator with symbol?(|ξ|).In the present paper,when the initial data f belongs to Sobolev space,we give the local and global weighted L~q estimate for the global maximal operator S?**defined by S?**f (x)=■where■is a formal solution of the equation (*).  相似文献   

7.
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.  相似文献   

8.
In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed.In this paper,we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces.With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space H q to the Hardy space H q for 0相似文献   

9.
In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L(logL)a(E1 × E2) for some a 〉 0, which is optimal.  相似文献   

10.
In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.  相似文献   

11.
In this article we are interested in conditions on the coefficients of a Walsh multiplier operator that imply the operator is bounded on certain dyadic Hardy spaces H p , 0 < p < ∞. In particular, we consider two classical coefficient conditions, originally introduced for the trigonometric case, the Marcinkiewicz and the Hörmander–Mihlin conditions. They are known to be sufficient in the spaces L p , 1 < p < ∞. Here we study the corresponding problem on dyadic Hardy spaces, and find the values of p for which these conditions are sufficient. Then, we consider the cases of H 1 and L 1 which are of special interest. Finally, based on a recent integrability condition for Walsh series, a new condition is provided that implies that the multiplier operator is bounded from L 1 to L 1, and from H 1 to H 1. We note that existing multiplier theorems for Hardy spaces give growth conditions on the dyadic blocks of the Walsh series of the kernel, but these growth are not computable directly in terms of the coefficients.  相似文献   

12.
This paper presents a weighted L 2 estimate with power weights for the maximal operator of commutators generated by compactly supported multipliers and Lipschitz functions. As an application, we study the almost convergence of the commutators, which is generated by the Bochner-Riesz means under the critical index and Lipschitz functions, for functions in L p (p ⩾ 2).  相似文献   

13.
Simon [J. Approxim. Theory, 127, 39–60 (2004)] proved that the maximal operator σα,κ,* of the (C, α)-means of the Walsh–Kaczmarz–Fourier series is bounded from the martingale Hardy space H p to the space L p for p > 1 / (1 + α), 0 < α ≤ 1. Recently, Gát and Goginava have proved that this boundedness result does not hold if p ≤ 1 / (1 + α). However, in the endpoint case p = 1 / (1 + α ), the maximal operator σα,κ,* is bounded from the martingale Hardy space H 1/(1+α) to the space weak- L 1/(1+α). The main aim of this paper is to prove a stronger result, namely, that, for any 0 < p ≤ 1 / (1 + α), there exists a martingale fH p such that the maximal operator σα,κ,* f does not belong to the space L p .  相似文献   

14.
The Carleson maximal operator is shown to be bounded inL p (w) for certain values ofp and certain radial weightsw when acting on products of radial functions and homogeneous harmonic polynomials. Partially supported by DGICYT (MEC Spain). PB 92/187.  相似文献   

15.
We obtain sharp estimates for some multilinear commutators related to certain sublinear integral operators. These operators include the Littlewood-Paley operator and Marcinkiewicz operator. As an application, we obtain weighted L p (p > 1) inequalities and an L log L-type estimate for multilinear commutators. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1419–1431, October, 2007.  相似文献   

16.
The d-dimensional classical Hardy spaces Hp(T d) are introduced and it is shown that the maximal operator of the Riemann sums of a distribution is bounded from Hp(T d) to Lp(T 2) (d/(d+1)<p≤∞) and is of weak type (1,1) provided that the supremum in the maximal operator is taken over a positive cone. The same is proved for the conjugate Riemann sums. As a consequence we obtain that every function f∈L1(T d) is a. e. Riemann summable to f, provided again that the limit is taken over a positive cone. This research was partly supported by the Hungarian Scientific Research Funds (OTKA) No F019633.  相似文献   

17.
We give a formula for the one-parameter strongly continuous semigroups ${e^{-tL^{\lambda}}}We give a formula for the one-parameter strongly continuous semigroups e-tLl{e^{-tL^{\lambda}}} and e-t [(A)\tilde]{e^{-t \tilde{A}}}, t > 0 generated by the generalized Hermite operator Ll, l ? R\{0}{L^{\lambda}, \lambda \in {\bf R}\backslash \{0\}} respectively by the generalized Landau operator ?. These formula are derived by means of pseudo-differential operators of the Weyl type, i.e. Weyl transforms, Fourier-Wigner transforms and Wigner transforms of some orthonormal basis for L 2(R 2n ) which consist of the eigenfunctions of the generalized Hermite operator and of the generalized Landau operator. Applications to an L 2 estimate for the solutions of initial value problems for the heat equations governed by L λ respectively ?, in terms of L p norm, 1 ≤ p ≤ ∞ of the initial data are given.  相似文献   

18.
 The one- and two-parameter Walsh system will be considered in the Paley as well as in the Kaczmarz rearrangement. We show that in the two-dimensional case the restricted maximal operator of the Walsh–Kaczmarz (C, 1)-means is bounded from the diagonal Hardy space H p to L p for every . To this end we consider the maximal operator T of a sequence of summations and show that the p-quasi-locality of T implies the same statement for its two-dimensional version T α. Moreover, we prove that the assumption is essential. Applying known results on interpolation we get the boundedness of T α as mapping from some Hardy–Lorentz spaces to Lorentz spaces. Furthermore, by standard arguments it will be shown that the usual two-parameter maximal operators of the (C, 1)-means are bounded from L p spaces to L p if . As a consequence, the a.e. convergence of the (C, 1)-means will be obtained for functions such that their hybrid maximal function is integrable. Of course, our theorems from the two-dimensional case can be extended to higher dimension in a simple way. (Received 20 April 2000; in revised form 25 September 2000)  相似文献   

19.
《偏微分方程通讯》2013,38(7-8):1267-1279
Abstract

We study L 2 harmonic p-forms on conformally compact manifolds with a rather weak boundary regularity assumption. We proved that if the lower bound of the curvature operator is great than or equal to ?1 and the infimum of the L 2 spectrum of the Laplacian great than p(n ? p) for some p ≤ n/2, then there is no nontrivial L 2 harmonic p-form.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号