T1 theorem for Besov and Triebel-Lizorkin spaces

Using the discrete Calderon type reproducing formula and the PlancherelPolya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved.     

Tl theorem for Besov and Triebel-Lizorkin spaces

Using the discrete Calderon type reproducing formula and the Plancherel-Polya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved.     

Characterizations for Besov spaces and applications. Part I

The main theorem of this paper gives a characterization for holomorphic Besov space B^p(D) over a large class of bounded domains D in , which states that there is a bounded linear operator so that PV_D=I on B^p(D), where P is the Bergman projection, and is the biholomorphic invariant measure with K(z,z) being Bergman kernel function for D. Moreover, some application for characterizing Schatter von Neumann p-class small Hankel operation is given as a direct consequence of this theorem.     

Generalized Besov spaces and Triebel-Lizorkin spaces

In this paper the classical Besov spaces Bsp.q and Triebel-Lizorkin spaces Fsp.q for s ∈R are generalized in an isotropy way with the smoothness weights {|2j|aln}∞j=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by Bap.q and Fap.q for a ∈Irk and k ∈N, respectively, keep many interesting properties, such as embedding theorems (with scales property for all smoothness weights), lifting properties for all parameters a, and duality for index 0 < p < ∞. By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between Bs,p.q and ∪tsBt,p.q,and between Fsp.q and ∪ts Ftp.q, respectively. Between Bs,p,q and ∪tsBt,p.qq,and between Fsp,qand ∪tsFtp.q,respectively.     

Isometric composition operators on the analytic Besov spaces

We investigate the isometric composition operators on the analytic Besov spaces. For 1<p<2$1<p<2$ we show that an isometric composition operator is induced only by a rotation of the disk. For p>2$p>2$, we extend previous work on the subject. Finally, we analyze this same problem for the Besov spaces with an equivalent norm.     

Decomposition of Besov and Triebel-Lizorkin spaces on the sphere

A discrete system of almost exponentially localized elements (needlets) on the n-dimensional unit sphere Sn is constructed. It shown that the needlet system can be used for decomposition of Besov and Triebel-Lizorkin spaces on the sphere. As an application of Besov spaces on Sn, a Jackson estimate for nonlinear m-term approximation from the needlet system is obtained.     

Besov type function spaces defined on metric-measure spaces

The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces.     

Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces

Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces by atoms,molecules and wavelets are given.These results generalize the corresponding results for classical Besov and Triebel-Lizorkin spaces.     

New characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type

In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for R^n.     

Toeplitz operators related to strongly singular Calderón-Zygmund operators

In this paper, the boundedness of Toeplitz operator T _b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε (ℝⁿ) is discussed from L ^p(ℝⁿ) to L ^q(ℝⁿ), , and from L ^p(ℝⁿ) to Triebel-Lizorkin space . We also obtain the boundedness of generalized Toeplitz operator Θ _α0 ^b from L ^p(ℝⁿ) to L ^q(ℝⁿ), . All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator T _b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L ^p(ℝⁿ), 1 < p < ∞.     

Riemann–Stieltjes operators between α ‐Bloch spaces and Besov spaces

We study the following two integral operators where g is an analytic function on the open unit disk in the complex plane. The boundedness and compactness of these two operators between the α ‐Bloch space B^α and the Besov space are discussed in this paper (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

<Emphasis Type="Italic">T</Emphasis>1 theorem for Besov and Triebel-Lizorkin spaces

Using the discrete Calderon type reproducing formula and the Plancherel-Polya characterization for the Besov and Triebel-Lizorkin spaces, theT1 theorem for the Besov and Triebel-Lizorkin spaces was proved.     

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].     

单位球上Besov空间的Toeplitz算子

考虑了全纯Besov空间B_p上的Toeplitz算子T_μ~α,这里μ是单位球上的一个复Borel测度.给出了T_μ~α在B_p上有界的一些充要条件.     

Boundedness of Multilinear Operators in Herz-type Hardy Space

Let κ∈ℕ. We prove that the multilinear operators of finite sums of products of singular integrals on ℝⁿ are bounded from HK ^α1,p1 _q1 (ℝⁿ) ×···×HK ^αk,pk _qk (ℝⁿ) into HK ^α,p _q (ℝⁿ) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α_j≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders. Received September 6, 1999, Revised November 17, 1999, Accepted December 9, 1999     

Maximal function characterizations of Hardy spaces on RD-spaces and their applications

Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a dimension n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] a...     

Multilinear Calderón-Zygmund Operators and Their Commutators with BMO Functions in Herz-Morrey Spaces with Variable Smoothness and Integrability

In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.