共查询到20条相似文献,搜索用时 109 毫秒
1.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
2.
The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, resDectivelv. 相似文献
3.
Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions. 相似文献
4.
5.
The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO. 相似文献
6.
TANG Sufang WEI Na 《偏微分方程(英文版)》2010,(1):1-15
In this paper, by establishing the boundedness of singular integral operators with variable kernels and their commutators with BMO functions on Morrey spaces of homogeneous groups, we prove a local a prior estimate in Sobolev-Morrey space for solutions to the nondivergence parabolic equation with discontinuous coefficients. 相似文献
7.
In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1, 0) in the sense of Ho¨rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces. 相似文献
8.
Zhenqian Li 《中国科学 数学(英文版)》2024,(5):951-974
In this article, we introduce multiplier ideal sheaves on complex spaces with singularities(not necessarily normal) via Ohsawa’s extension measure, as a special case of which, it turns out to be the socalled Mather-Jacobian multiplier ideals in the algebro-geometric setting. Inspired by Nadel’s coherence and Guan-Zhou’s strong openness properties of the multiplier ideal sheaves, we discuss similar properties for the generalized multiplier ideal sheaves. As applications, we obtain a reasonable ge... 相似文献
9.
In this paper, the boundedness of an oscillating multiplier m γ,β for different β on the Herz type spaces is obtained. This operator was initially studied by Wainger and Fefferman-Stein. Our results extend one of the main results in a paper by Xiaochun Li and Shanzhen Lu for the non-weighted case, if β is close to 1 or α is suitably large. For β ≥ 1, the results with no weights on the Herz type spaces are also new. 相似文献
10.
In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces V W L_Π~(p,φ)(?) with bounded set ?. 相似文献
11.
12.
Yohei Tsutsui 《Journal of Fourier Analysis and Applications》2011,17(2):265-289
In this note we establish the sharp maximal inequalities for Herz spaces and Morrey spaces by use of good ??-inequality. As an application, we obtain estimates of some bilinear forms which include usual product of functions and the nonlinear term of Euler and Navier-Stokes equations on Herz spaces and Morrey spaces. 相似文献
13.
Qi Zhang & Jiman Zhao 《分析论及其应用》2020,36(2):200-216
In this paper, we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups, involving weighted Lebesgue spaces, classical Morrey spaces and central Morrey spaces. Meanwhile, some necessary and sufficient conditions of boundness are obtained. 相似文献
14.
假定T_σ是关于乘子σ的双线性Fourier乘子算子,其中σ满足如下Sobolev正则条件:对某个s∈(n,2n],有sup_(κ∈Z)‖σ_k‖W~s(R~(2m))∞.对于p_1,p_2,p∈(1,∞)且满足1/p=1/p_1+1/p_2和ω=(ω_1,ω_2)∈A_(p/t)(R~(2n)),建立了T_σ及其与函数b=(b_1,b_2)∈(BMO(R~n))~2生成的交换子T_(σ,b)由L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的有界性;同时,在b_1,b_2∈CMO(R~n)(C_c~∞(R~n)在BMO拓扑下的闭包)的条件下,证明交换子T_(σ,b)是L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的紧算子.为了得到主要结果,我们先后建立了几个双(次)线性极大函数在加多权Morrey空间上的有界性以及该空间中准紧集的判定. 相似文献
15.
In this paper, we consider multipliers from Sobolev spaces to Lebesgue spaces. We establish some wavelet characterization of multiplier spaces without using capacity. Further, we give a sharp logarithmic Morrey space condition for multipliers which lessens Fefferman’s Morrey space condition to the logarithm level and generalizes Lemarié’s counter-example to non-integer cases and expresses his results in a more precise way. 相似文献
16.
In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds. 相似文献
17.
Frédéric Bernicot Diego Maldonado Kabe Moen Virginia Naibo 《Journal of Geometric Analysis》2014,24(2):1144-1180
The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato–Morrey spaces under Sobolev scaling. 相似文献
18.
Zujin Zhang 《Journal of Mathematical Analysis and Applications》2011,375(2):799-802
We study the Cauchy problem for the generalized MHD equations, and prove some regularity criteria involving the integrability of ∇u in the Morrey, multiplier spaces. 相似文献
19.
Maria Alessandra Ragusa 《Journal of Global Optimization》2008,40(1-3):361-368
In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey
spaces VL
p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal
function and the fractional maximal function and related Morrey inequalities.
相似文献
20.
Yoshihiro Sawano 《Mathematische Nachrichten》2010,283(10):1456-1487
The purpose of this paper is to develop a theory of the Besov‐Morrey spaces and the Triebel‐Lizorkin‐Morrey spaces on domains in R n. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains in R n we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p, q in the Morrey space ??pq (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献