Strongly Singular Calderon-Zygmund Operator and Commutator on Morrey Type Spaces

In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.     

一类带奇异低阶项椭圆型方程的正则性

本文得到了一类带奇异低阶项椭圆方程的一个正则性结果.方程形式为Lu+ vu=μ,其中L为二阶散度型椭圆算子,v属于某一Morrey空间,μ为一非负Radon 测度.     

Boundedness of the solutions to non-linear systems with Morrey data

We consider non-linear elliptic systems satisfying componentwise coercivity condition. The non-linear terms have controlled growths with respect to the solution and its gradient, while the behaviour in x is governed by functions in Morrey spaces. We firstly prove essential boundedness of the weak solution and then we obtain Morrey regularity of its gradient.     

Existence and large time behavior to coupled chemotaxis-fluid equations in Besov–Morrey spaces

The paper deals with the Cauchy problem of coupled chemotaxis-fluid equations. By taking advantage of a coupling structure of the equations and using the semigroup approach, we show existence and asymptotic stability with small initial data and external force $(u_0,n_0,\mathrm{?}{c}_0,c_0)\in {\dot{\mathbf{N}}}_{r_1,\lambda ,\infty }^{?{\beta }_1}\times {\dot{\mathbf{N}}}_{r_2,\lambda ,\infty }^{?{\beta }_2}\times {\dot{\mathbf{N}}}_{r_3,\lambda ,\infty }^{?{\beta }_3}\times L^{\infty },\mathrm{?}?\in M_{N?\lambda ,\lambda }$ for certain technical assumptions. For the embedded relationship between function spaces, we show that our initial data class is larger than that of Kozono et al. (2016) [11] and covers physical cases of initial aggregation at points (Diracs) and on filaments. As an application, we obtain a class of asymptotically existence of a basin of attraction for each self-similar solutions with homogeneous initial data.     

λ-central BMO estimates for commutators of singular integral operators with rough kernels

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.     

Sparse non-smooth atomic decomposition of Morrey spaces

Recently, a non-smooth atomic decomposition in Morrey spaces was obtained by the author, Iida and Tanaka. This note refines the above existing result using the notion of sparse families. As an application, we prove the equivalence between fractional integral operators and fractional maximal operators under the Morrey norm.     

Fourier–Jacobi expansions in Morrey spaces

In this paper we obtain a characterization of the convergence of the partial sum operator related to Fourier–Jacobi expansions in Morrey spaces.     

Parabolic equations with VMO coefficients in generalized Morrey spaces

In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means of the theory of singular integrals and linear commutators.     

分数次积分交换子在非齐Morrey空间上的紧性

本文主要建立由分数次积分$I_{\gamma}$与函数$b\in\mathrm{Lip}_{\beta}(\mu)$生成的交换子$[b, I_{\gamma}]$在以满足几何双倍与上部双倍条件的非齐度量测度空间为底空间的Morrey空间上紧性的充要条件.在假设控制函数$\lambda$满足逆双倍条件下,证明了交换子$[b,I_{\gamma}]$为从Morrey空间$M^{p}_{q}(\mu)$到$M^{s}_{t}(\mu)$紧性当且仅当$b\in\mathrm{Lip}_{\beta}(\mu)$.