Strong type estimate and Carleson measures for Lipschitz spaces

We establish a capacitary strong type estimate for Lipschitz space and characterize the related Carleson measures.

     

Carleson embedding theorem on convex finite type domains

This paper concerns certain geometric aspects of function theory on smoothly bounded convex domains of finite type in Cn. Specifically, we prove the Carleson-Hörmander inequality for this class of domains and provide examples of Carleson measures improving a known result concerning such measures associated to bounded holomorphic functions.     

Carleson and Vanishing Carleson Measures on Radial Trees

We extend a discrete version of an extension of Carleson’s theorem proved in [5] to a large class of trees that have certain radial properties. We introduce the geometric notion of s-vanishing Carleson measure on such a tree T (with s ≥ 1) and give several characterizations of such measures. Given a measure σ on T and p ≥ 1, let L ^p (σ) denote the space of functions g defined on T such that |g| ^p is integrable with respect to σ and let L ^p (? T) be the space of functions f defined on the boundary of T such that |f| ^p is integrable with respect to the representing measure of the harmonic function 1.We prove the following extension of the discrete version of a classical theorem in the unit disk proved by Power. A finite measure σ on T is an s-vanishing Carleson measure if and only if for any real number p > 1, the Poisson operator P : L ^p (? T) → L ^sp (σ) is compact. Characterizations of weak type for the case p = 1 and in terms of the tree analogue of the extended Poisson kernel are also given. Finally, we show that our results hold for homogeneous trees whose forward probabilities are radial and whose backward probabilities are constant, as well as for semihomogeneous trees.     

Holomorphic Campanato type spaces over Carleson tubes and Bergman metric balls

In this paper we give some characterizations of holomorphic Campanato type spaces in terms of Carleson tubes and Bergman metric balls in the unit ball.     

Weighted BMO and Carleson measures on spaces of homogeneous type

In this paper we characterize the weighted BMO(ω)(X), with X a space of homogeneous type, through an adequate weighted Carleson measure. As a byproduct we can define the weighted Triebel-Lizorkin space and obtain the identification with the above space.     

Carleson measures, multipliers and integration operators for spaces of Dirichlet type

For 0<p<∞ and α>−1, we let denote the space of those functions f which are analytic in the unit disc and satisfy . In this paper we characterize the positive Borel measures μ in D such that , 0<p<q<∞. We also characterize the pointwise multipliers from to (0<p<q<∞) if p−2<α<p. In particular, we prove that if the only pointwise multiplier from to (0<p<q<∞) is the trivial one. This is not longer true for and we give a number of explicit examples of functions which are multipliers from to for this range of values.     

Carleson type estimates for second order elliptic equations with unbounded drift

We derive a Carleson type estimate for positive solutions of non-divergence second order elliptic equations Lu = a _ij D _ij u + b _i D _i u = 0 in a bounded domain Ω ⊂ ℝ ⁿ . We assume that b _i ∈ L ⁿ (Ω) and Ω is a twisted H?lder domain of order α ∈ (1/2, 1] which satisfies a weak regularity condition. We also provide an example which shows that the main result fails in general if α ∈ (0, 1/2]. Bibliography: 18 titles.     

Carleson测度和多项式逼近

设G是复平面C上的单连通区域,在研究G上的Carleson测度和多项式在G上的Hardy空间Hq(G)中的稠密性问题时,建立起了两者之间的一种等价关系.用Carleson测度给出了多项式在Hq(G)中稠密的充要条件,也刻画了所有那些使得在其上的Carleson测度和Carleson不等式等价的单连通区域.     

Ahlfors-regular curves and Carleson measures

Science China Mathematics - We study the relation between the boundary of a simply connected domain Ω being Ahlfors-regular and the invariance of Carleson measures under the push-forward...     

Carleson测度和多项式逼近

设G是复平面C上的单连通区域,在研究G上的Carleson测度和多项式在G上的Hardy空间Hq(G)中的稠密性问题时,建立起了两者之间的一种等价关系．用Carleson测度给出了多项式在Hq(G)中稠密的充要条件,也刻画了所有那些使得在其上的Carleson测度和Carleson不等式等价的单连通区域．     

Some estimates for type and cotype constants

Mathematische Annalen -     

Dirichlet型空间的Carleson测度和乘子

设0-1,D_α~p表示单位球B_n上满足∫_(B_n)(1-|z|~2)~α|▽f(z)|~pdv(z)<∞的全纯函数全体.对0相似文献   

Number of Carleson sequences

This note is devoted to the refinement of a result of N. K. Nikol'skii and B. S. Pavlov (Ref. Zh. Mat. 1970, 6B678) describing the distribution of the discrete spectrum of a certain class of operators. Namely, one proves the following. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Mathematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 65, pp. 178–182, 1976.     

Carleson measures and vector-valued BMO martingales

We study the relationship between vector-valued BMO martingales and Carleson measures. Let ${(\Omega,\mathcal {F} ,P)}$ be a probability space and 2 ≤ q < ∞. Let X be a Banach space. Given a stopping time τ, let ${\widehat{\tau}}$ denote the tent over τ: $$\widehat{\tau}=\{(w,k)\in \Omega\times \mathbb {N}: \tau(w)\leq k, \tau(w) < \infty\}.$$ We prove that there exists a positive constant c such that $$\sup_{\tau}\frac{1}{P(\tau < \infty)}\int \limits_{{\widehat{\tau}}}\|df_k\|^qdP\otimes dm\leq c^q\|f\|_{BMO(X)}^q$$ for any finite martingale with values in X iff X admits an equivalent norm which is q-uniformly convex. The validity of the converse inequality is equivalent to the existence of an equivalent p-uniformly smooth norm. And then we also give a characterization of UMD Banach lattices.     

A note on Markov type constants

We prove that, if a geodesic metric space has Markov type 2 with constant 1, then it is an Alexandrov space of nonnegative curvature. The same technique provides a lower bound of the Markov type 2 constant of a space containing a tripod or a branching point. Received: 28 November 2007     

Sharp constants in hardy type inequalities

We prove new weighted Hardy type inequalities with sharp constants and describe their applications to inequalities in multidimensional domains.     

Carleson Measures via BMO

We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated with the given measure in a natural way. This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).     

On some estimates and Carleson type measure for multifunctional holomorphic spaces in the unit ball

The aim of this paper is to obtain some new estimates for multifunctional holomorphic expressions by using properties of Bergman metric ball. Also we obtain some characterizations of Carleson type measure for some multifunctional holomorphic spaces defined with Bergman metric ball.     

Carleson measures and the heat equation

Let { }, where { } is the open unit disk on the complex plane { }. In G, we consider analytic solutions u(t, z) ({ }, { }) of the heat equation 2u_t=u_zz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have { } Bibliography: 17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155. Translated by S. V. Kislyakov.