REVERSE CARLESON MEASURES ON GENERALIZED FOCK SPACES

In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).

CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF C^n

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bp^σ（B） and p-Carleson measure in the unit ball of C^n. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on Bp（B） spaces by means of Carleson measures for Bp^σ（B）.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

CARLESON MEASURES AND THE GENERALIZED CAMPANATO SPACES OF VECTOR-VALUED MARTINGALES

In this paper, the so-called（p,Ф）-Carleson measure is introduced and the rela-tionship between vector-valued martingales in the general Campanato spaces Lp,Ф（X） and the （p, Ф）-Carleson measures is investigated. Specifically, it is proved that for q ∈ [2, ∞）, the measure d# ：-=││ dfk││^qdP dm is a （q, Ф）-Carleson measure on Ω × N for every f ∈ Lq,Ф（X） if and only if X has an equivalent norm which is q-uniformly convex; while for p C （1, 2], the measure dμ ：=││dfk││^pP dm is a （p, Ф）-Carleson measure on Ω ×N implies that f ∈ Lp,Ф（X） if and only if X admits an equivalent norm which is p-uniformly smooth. This result extends an earlier result in the literature from BMO spaces to general Campanato spaces.

D_(K) SPACES AND CARLESON MEASURES

We give some characterizations of Carleson measures for Dirichlet type spaces by using Hadamard products.We also give a one-box condition for such Carleson measures.

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

In this paper,we give a survey of some recent progress in terms of verifying Carleson measures;this includes the difference between two definitions of a Carleson measure,the Bergman tree condition,the T1 condition for Besov-Sobolev spaces on a complex ball,vector-valued Carleson measures,Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.

α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C^n

In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.

Toeplitz Operators and Carleson Measures for Weighted Bergman Spaces Induced by Regular Weights

In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1<p,q<∞andω,η,υare regular weights.By using Khinchin’s inequality and Kahane’s inequality,we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.

Carleson Measure Associated with the Fractional Heat Semigroup of Schrodinger Operator

Let L=-△+V be a Schrodinger operator,where△is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Holder class Ba/2.In this paper,we define a new version of Carleson measure associated with the fractional heat semigroup of Schrodinger operator L.We will characterize the Campanato spaces and the predual spaces of the Hardy spaces by the new Carleson measure.

Carleson Measure Characterization of Bloch Functions

We give several equivalences of Bloch functions and little Bloch funetions.Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions,that is,f ∈ B if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized Carleson measure; f ∈ B0 if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized vanishing Carleson measure,where Dβf（β】0）is the fractional derivative of analytic function f of order β,m denotes the normalised Lebesgue measure.

Ahlfors-regular curves and Carleson measures

We study the relation between the boundary of a simply connected domainΩbeing Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk△onto the domainΩ.As an application,we characterize the chord-arc curves with small norms and the asymptotically smooth curves in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.

Carleson Measures on the Weighted Bergman Spaces with Békollé Weights

In this paper,the authors characterize Carleson measures for the weighted Bergman spaces with Békollé weights on the unit ball.They apply the Carleson embedding theorem to study the properties of Toeplitz-type operators and composition operators acting on such spaces.

Carleson Measures on Planar Sets

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets

Dual Space, Carleson Measure and Sequence Interpolation on A^p(φ)(0

Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.

A DERIVATIVE-HILBERT OPERATOR ACTING ON HARDY SPACES

Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,where f(z)=∞∑n=0a_(n)z^(n) is an analytic function in D.We characterize the positive Borel measures on[0,1)such thatDHμ(f)(z)=f[0,1)f(t)/(1-tz)^(2)dμ(t) for all f in the Hardy spaces Hp(0<p<∞),and among these we describe those for which is a bounded(resp.,compact)operator from Hp(0<p<∞)into Hq(q>p and q≥1).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).

COMPOSITION OPERATORS FROM B^a TO F(p,q,s)

Necessary and sufficient conditions are given for a composition operator Cof = f o o to be bounded and compact from Ba to F(p, q, s).

A REPRESENTATION THEOREM OF HARMONIC FUNCTIONS AND ITS APPLICATION TO BMO ON MANIFOLDS

In this paper a representation theorem of harmonic functions on manifolds is set up. As an application, a characterization of BMO in terms of Carleson measures is obtained.

Toeplitz Operators on the Bergman Space of Multi-connected Domains

In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.

EXTENDED CESRO OPERATORS AND MULTIPLIERS ON BMOA

In this article, we characterize the boundedness and compactness of extended Cesaro operators on the spaces BMOA by the Carleson measures in the unit ball. Mea while, we study the pointwise multipliers on BMOA.

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF C^n

This article is devoted to studying the decomposition of functions of Qp spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Qp spaces with small scale p, n-1/n〈 p ≤ 1 by means of p-Carleson measure and the Bergman metric on the unit ball of Cn. At the same time, a decomposition theorem for Qp,O spaces is given as well.