BOUNDEDNESS OF CALDERN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION

In this article, the author introduces a class of non-convolution Calder′on-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces ■p0 ,q(1 ≤p,q ≤∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hrmander condition can ensure the boundedness of convolution-type Calder′on-Zygmund operators on Besov spaces ■p0 ,q(1 ≤p,q ≤∞). However, the proof is quite different from the previous one.     

Besov 空间上的算子插值定理

本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理.     

WELL-POSEDNESS IN CRITICAL SPACES FOR THE FULL COMPRESSIBLE MHD EQUATIONS

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.     

BESOV SPACES B_p~(α,p) ON DOMAINS AND LAPLACE OPERATORS

Let fi be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpa,p on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.     

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

DIRECT AND INVERSE THEOREMS FOR JACKSON MEANS OF ENTIRE EXPONENTIAL TYPE IN Ba SPACES

This paper presents a new type of interpolation of B_a spaces, with which a new characterization of B_a spaces by the Jackson means of entire exponential type is given.     

Function spaces of varying smoothness I

This paper deals with function spaces of varying smoothness. It is a modified version of corresponding parts of [8]. Corresponding spaces of positive smoothness s (x) will be considered in part II. We define the spaces B_p (?ⁿ ), where the function ??: x ? s (x) is negative and determines the smoothness pointwise. First we prove basic properties and then we use different wavelet decompositions to get information about the local smoothness behavior. The main results are characterizations of the spaces B_p (?ⁿ ) by weighted sequence space norms of the wavelet coefficients. These assertions are used to prove an interesting connection to the so‐called two‐microlocal spaces C^{s,s ′} (x⁰). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

COMPOSITION OPERATORS ON BERGMAN SPACES＊＊＊

The authors obtain function theoretic characterizations of the compactness on the Standard weighted Bergman spaces of the two operators formed by multiplying a composition operator with the adjoint of another composition operator.     

Spaces of Besov-Sobolev type and a problem on nonlinear approximation

We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space ${\dot{W}}^{1,p}$. The resulting spaces are identified as a special class of real interpolation spaces of Sobolev-Slobodecki? spaces. We establish the equivalence between Fourier analytic definitions and definitions via difference operators acting on measurable functions. We prove various new results on embeddings and non-embeddings, and give applications to harmonic and caloric extensions. For suitable wavelet bases we obtain a characterization of the approximation spaces for best n-term approximation from a wavelet basis via smoothness conditions on the function; this extends a classical result by DeVore, Jawerth and Popov.     

A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES

In this paper, a characterization of orthonormal wavelet families in Sobolev spaces H s (R) is established.     

Calderon-Zygmund型算子在加权Herz型Hardy空间上的弱型估计

本文引入了加权弱Herz型Hardy空间，并证明了当a=n(1-1/q) δ时，胡国恩和陆善镇等在文[1]中所考虑的两类Calderon-Zygmund型算子分别连续地映加权Herz型Hardy空间到加权弱Herz空间和加权弱Herz型Hardy空间。     

DECOMPOSITION FOR BERS-ORLICZ SPACES

ＤＥＣＯＭＰＯＳＩＴＩＯＮＦＯＲＢＥＲＳ－ＯＲＬＩＣＺＳＰＡＣＥＳＺｈａｏＲｕｈａｎ（赵如汉）（ＷｕｈａｎＩｕｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＡｃａｄｒｍｉａＳｉｎｄａ．，Ｗｕｈａｎ４３００７１，Ｃｈｉｎａ．）ＤＥＣＯＭＰＯＳＩＴＩＯＮＦＯＲＢＥＲＳ－...     

推广的Q空间

Q空间(或Qp,或Qα空间)的研究受到许多研究者的关注.最近,Wu和Xie将Q空间推广到Qpα,q空间.本文对一般的Q空间进行研究.首先,表明某些实变量刻画和小波刻画的等价性,主要想法是用2n维小波分析属于n维空间Rn的Qpα,q中的元素.其次,也构造出了空间Qpα,q的预对偶空间Ppα,q,其中Ppα,q是由小波定义的原子生成.     

New bases for Triebel-Lizorkin and Besov spaces

We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin and Besov spaces. These include the , , potential, and Sobolev spaces. The main feature of our method is that the character of the basis functions can be prescribed in a very general way. In particular, if is any sufficiently smooth and rapidly decaying function, then our method constructs a basis whose elements are linear combinations of a fixed (small) number of shifts and dilates of the single function . Typical examples of such 's are the rational function and the Gaussian function This paper also shows how the new bases can be utilized in nonlinear approximation.

     

Boundedness of the θ-type Calderon-Zygmund Operators on Weighted Herz-type

In this paper, we will discuss the boundedness of θ-type Calderdn-Zygmund operator on weighted Herz-type Hardy spaces.     

Calderón——Zygmund 型算子及其交换子的有界性

本文得到了Calderón--Zygmund型算子及其与BMO函数或Lipschitz函数生成的交换子在Herz 型 Hardy空间上的一些有界性结果.     

GENERAL OPEN MAPPING THEOREMS FOR LINEAR TOPOLOGICAL SPACES

0IntroductionIntile1930's,thefirstoped1flappingtheoremforFr6clletspaceswasprovedbyS.B....htll].Sincethedtilevariousextellsiollsoftheopenmappingtheoremhaveapl)earedillsuccessiollforitsapplications(fordetails,see[4]).In1958,V.PtAkfoundoutthatoped1llappillgtheoremsareconllectedwithsolllecompleteness,alldheobtainedastrikillgextensiollofBallach'sclassicaltlleoreul,whichpoilltsoutthatcontinuouslillearmapsfi.olllB-colllpletespacesolltobarrelledspacesareoped['].1111965,T.Husaingaveaninlportalltope…     

Bilinear estimate on tent‐type spaces with application to the well‐posedness of fluid equations

We introduce a class of tent‐type spaces and establish a Poisson extension result of Triebel–Lizorkin spaces . As an application, we get the well‐posedness of Navier–Stokes equations and magnetohydrodynamic equations with initial data in critical Triebel–Lizorkin spaces , . Copyright © 2016 John Wiley & Sons, Ltd.     

On the Libera operator

We show that the Libera operator, L, on some spaces of analytic functions is a continuous extension of the conjugate of the Cesàro operator. Results on L acting on various spaces are obtained. In particular, L maps the Bloch space into BMOA. We also prove some results on the best approximation by polynomials in Hardy and Bergman spaces.