Inhomogeneous Besov and Triebel-Lizorkin spaces associated with a para-accretive function and their applications

In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.

APPLICATIONS OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES

In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.

A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS

In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.

Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces

In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.

Function spaces of Besov-type and Triebel-Lizorkin-type——a survey

This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS FROM L^p(R^n) TO TRIEBEL-LIZORKIN SPACES

Let b^→=（b1,…,bm）,bi∈∧°βi（R^n）,1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f（x）=∫R^n（b1（x）-b1（y））…（bm（x）-bm（y））K（x-y）f（y）dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p（R^n） to Fp^β,∞（R^n）,as well as [b^→,1α]form L^p （R^n） to Fp^β,∞（R^n）,where 1/q=1/p-α/n.

DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES

In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that （Fp＇q）＊ = CMOp^-a,q＇ for 0 ~p≤ 1.

BOUNDEDNESS OF PARABOLIC SINGULAR INTEGRALS AND MARCINKIEWICZ INTEGRALS ON TRIEBEL-LIZORKIN SPACES

In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.

A CLASS OF OSCILLATORY SINGULAR INTEGRALS ON TRIEBEL-LIZORKIN SPACES

The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.

Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences

Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.

THE BESOV AND TRIEBEL-LIZORKIN SPACES WITH HIGH ORDER ON THE LIPSCHITZ CURVES

The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also.

WAVELET CHARACTERIZATION OF WEIGHTED TRIEBEL-LIZORKIN SPACES

In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces. Our weights belong to the Muckenhoupt class A q and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.

Boundedness of Fractional Integrals with a Rough Kernel on the Product Triebel-Lizorkin Spaces

By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.

A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES

Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R.

Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces

In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.

Certain averaging operators on Triebel-Lizorkin spaces

In this article,we study the boundedness properties of the averaging operator S_(t)^(γ) on Triebel-Lizorkin spaces F_(p,q)^(α)(R^(n))for various p,q.As an application,we obtain the norm convergence rate for S_(t)^(γ)(f)on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_(t)^(γ) is given.

A NEW KIND OF SPACES OF TRIEBEL-LIZORKIN TYPE

In this note,we define a new kind of spaces TF of Triebel-Lizorkin type and characterize it via sequence space lp Also a Fourier multiplier theorem is established in this new spaces TFpaq

Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces

In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-1） and some class WFα（S^n-1）, which relates to Grafakos-Stefanov class. Some previous results are extended and improved.

An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.