Calderón-Zygmund算子在H_b~p空间上的有界性

众所周知,如果Calderón-Zygmund算子T满足T~*(1)=0,则算子T在H~p,n/(n+ε)相似文献   

p-adic域,p-级数域的整环子群上微积分算子的Hardy空间有界性

Ｆ．Ｓｃｈｉｐｐ和Ｗ．Ｒ．Ｗａｄｅ在［１］中证明了单位方体上Ｄｙａｄｉｃ二元微积分算子的混合Ｈａｒｄｙ空间Ｈ＃（Ｉ×Ｉ）的弱型．本文证明了ｐ ａｄｉｃ域，ｐ 级数域的整环子群上一元和二元积分算子与微积分算子的Ｈｒ（Ｇ）与Ｈ＃（Ｇ×Ｇ）（０＜ｒ１）有界性．     

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.     

The molecular characterization of weighted Hardy spaces

The molecular characterization of the weighted atomic Hardy space H_w ^p,q,s is given. As an application, the boundedness of Hilbert transform on the weighted Hardy space is proved.     

Superposition Operators in the Algebra of Functions of Two Variables with Finite Total Variation

 We show that the Hardy space of functions of two variables with finite total variation is a Banach algebra under the pointwise operations and a suitably chosen norm. Then we characterize Nemytskii superposition operators, which map the Hardy space into itself and satisfy the global Lipschitz condition. Received 7 June 2001; in revised form 8 January 2002     

Hardy spaces on the Quaternions

In this paper, the Quaternion-valued Hardy spaces and conjugate Hardyspaces on are characterized. In analogy with the decomposition of square-integrable function space on the real line into the direct sum of Hardy space and conjugate Hardy space, the square-integrable Quaternion -valued function space on is decomposed into the orthogonal sum of the Quaternion Hardy and conjugate Hardy spaces.     

Potential Operators in Weighted Herz-Type Spaces over Locally Compact Vilenkin Groups

Let G be a bounded locally compact Vilenkin group. We study the boundedness of potential operators and the maximal operators associated with them in the weighted Herz space, the weighted Hardy space and the weighted Herz-type Hardy space over G. We also discuss the boundedness of these operators on the weighted weak Lebesgue space and the weighted weak Herz space whose sharpness are also discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Subnormality and composition operators on the Bergman space

Following the work of C. Cowen and T. Kriete on the Hardy space, we prove that under a regularity condition, all composition operators with a subnormal adjoint on A²(D) have linear fractional symbols of the form. Moreover, we show that all composition operators on the Bergman space having these symbols have a subnormal adjoint, with larger range for the parameterr than found in the Hardy space case.     

On Hardy and BMO Spaces for Grushin Operator

We study Hardy and BMO spaces associated with the Grushin operator. We first prove atomic and maximal functions characterizations of the Hardy space. Further we establish a version of Fefferman–Stein decomposition of BMO functions associated with the Grushin operator and then obtain a Riesz transforms characterization of the Hardy space.     

Weighted Composition Operators between Different Hardy Spaces

Let and be two analytic functions defined on such that. The operator given by is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from a Hardy space H _p into another Hardy space H _q . We apply these results to study composition operators on Hardy spaces of a half-plane. Submitted: November 20, 2001.     

Singular integral operator,Hardy–Morrey space estimates for multilinear operators and Navier–Stokes equations

After establishing the molecule characterization of the Hardy–Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy–Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier–Stokes equations for the initial data in the Hardy–Morrey space ????(p?n) for q as small as possible. Here, the Hardy–Morrey space estimates for multilinear operators are important tools. Copyright © 2010 John Wiley & Sons, Ltd.     

Behavior of Shannon’s Sampling Series for Hardy Spaces

In this paper the convergence behavior of the Shannon sampling series is analyzed for Hardy spaces. It is well known that the Shannon sampling series is locally uniformly convergent. However, for practical applications the global uniform convergence is important. It is shown that there are functions in the Hardy space such that the Shannon sampling series is not uniformly convergent on the whole real axis. In fact, there exists a function in this space such that the peak value of the Shannon sampling series diverges unboundedly. The proof uses Fefferman’s theorem, which states that the dual space of the Hardy space is the space of functions of bounded mean oscillation. This work was partly supported by the German Research Foundation (DFG) under grant BO 1734/9-1.     

A type theorem on the weighted Herz‐type Hardy spaces and applications

This paper gives a type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space.     

Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball

We investigate the weighted composition operator from the weighted Bergman space into the weighted Hardy space on the unit ball. As a consequence of the investigation, we also give a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space.     

Beurling type theorem on the Bergman space via the Hardy space of the bidisk

In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.     

Algebraic Properties of Dual Toeplitz Operators on Harmonic Hardy Space over Polydisc

In this paper,we introduce the harmonic Hardy space on T~n and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on T~n.     

Operator theory in the Hardy space over the bidisk (I)

In this paper, we identify the vector valued Hardy space with the Hardy space over the bidisk and construct a universal model for thecontractive analytic functions. We will also study some elementary properties of the submodules and show, in some cases, how the operator theoretical properties are related to the module theoretical properties. The last part focus on the study of double commutativity of compression operators.     

Calderón – Zygmund Operators on Weighted Weak Hardy Spaces in Locally Compact Vilenkin Groups

Let G be a bounded locally compact Vilenkin group. We study the atomic decom‐position of weighted weak Hardy space. We also define several Calderón – Zygmund type operators and study their boundedness on, spaces like weighted Hardy spaces, weighted weak Hardy spaces and weighted weak Lebesgue spaces. Sharpness of some of our results is also discussed.     

Uniqueness Properties of Hardy Space Functions

We study the boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.     

On the reflexivity of subspaces of Toeplitz operators on the hardy space on the upper half-plane

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ^∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L ¹ spaces.