共查询到20条相似文献,搜索用时 31 毫秒
1.
Dashan Fan 《Integral Equations and Operator Theory》1994,20(4):383-394
We obtain a weak type theorem of Calderón-Zygmund operators in the Hardy space. 相似文献
2.
James E. Daly 《Journal of Fourier Analysis and Applications》1999,5(4):303-308
Calderón-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderón-Zygmund convolution singular integral operator is bounded on the Hardy space H1 (Rn), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn–1) on the sphere. 相似文献
3.
Jizheng Huang 《Bulletin des Sciences Mathématiques》2009,133(6):588-596
In this paper, we will consider the boundedness of Weyl multiplier on Hardy spaces associated with twisted convolution. In order to get our result, we need to give some characterizations of the Hardy space associated with twisted convolution. Including Lusin area integral, Littlewood-Paley g-function. 相似文献
4.
Let be a mapping in the Sobolev space . We assume that the cofactors of the differential matrix Df(x) belong to . Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space .
Received: 20 November 2000 / Revised version: 17 December 2001 / Published online: 5 September 2002
Iwaniec was supported by NSF grant DMS-0070807. This research was done while Onninen was visiting Mathematics Department at
Syracuse University. He wishes to thank SU for the support and hospitality. 相似文献
5.
Hart F. Smith 《Journal of Geometric Analysis》1998,8(4):629-653
We introduce a new function space, denoted by H
FIO
1
(ℝn), which is preserved by the algebra of Fourier integral operators of order 0 associated to canonical transformations. A subspace
of L1 (ℝn), this space in many aspects resembles the real Hardy space of Fefferman-Stein. In particular, we obtain an atomic characterization
of H
FIO
1
(ℝn). In contrast to the standard Hardy space, these atoms are localized in frequency space as well as in real space. 相似文献
6.
A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form. 相似文献
7.
《Journal of Functional Analysis》2003,199(2):287-300
It is shown that an analytic map ? of the unit disk into itself inducing a Hilbert-Schmidt composition operator on the Dirichlet space has the property that the set has zero logarithmic capacity. We also show that this is no longer true for compact composition operators on the Dirichlet space. Moreover, such a condition is not even satisfied by Hilbert-Schmidt composition operators on the Hardy space. 相似文献
8.
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H2. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures. 相似文献
9.
Frédéric Bayart 《Monatshefte für Mathematik》2002,136(3):203-236
In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis tools. The space is an analogue for Dirichlet series of the space for Fourier series. We continue their study by introducing , an analogue to the spaces . Thanks to Bohr’s vision of Dirichlet series, we identify with the Hardy space of the infinite polydisk . Next, we study a variant of the Poisson semigroup for Dirichlet series. We give a result similar to the one of Weissler
([25]) about the hypercontractivity of this semigroup on the spaces . Finally, following [8], we determine the composition operators on , and we compare some properties of such an operator and of its symbol.
Received October 3, 2001; in revised form January 16, 2002 Published online July 12, 2002 相似文献
10.
Svante Janson 《Integral Equations and Operator Theory》1994,20(2):238-242
The quotient space of a Hardy space on a half-plane Imz> modulo the subspace of elements containing a factore
iz
is in some sense independent of . A formula is derived which exhibits a correspondence between any two such quotient spaces.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine. 相似文献
11.
Alexander E. Richman 《Integral Equations and Operator Theory》2003,45(1):105-124
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. 相似文献
12.
It is well-known that Calderón-Zygmund operators T are bounded on Hp for\(\frac{n}{{n + 1}}< p \leqslant 1\) provided T*(1) = 0. In this article, it is shown that if T*(b) = 0, where b is a para-accretive function, T is bounded from the classical Hardy space Hp to a new Hardy space H b p . To develop an H b p theory, a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequalities associated to a para-accretive function are established. Moreover, David, Journé, and Semmes’ result [9] about the LP, 1 < p < ∞, boundedness of the Littlewood-Paley g function associated to a para-accretive function is generalized to the case of p ≤ 1. A new characterization of the classical Hardy spaces by using more general cancellation adapted to para-accretive functions is also given. These results complement the celebrated Calderón-Zygmund operator theory. 相似文献
13.
《Mathematische Nachrichten》2017,290(17-18):2725-2739
In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball. 相似文献
14.
The atomic decomposition of Hardy spaces by atoms defined by rearrangement-invariant Banach function spaces is proved in this paper. Using this decomposition, we obtain the characterizations of BMO and Lipschitz spaces by rearrangement-invariant Banach function spaces. We also provide the sharp function characterization of the rearrangement-invariant Banach function spaces. 相似文献
15.
Oleh Lopushansky 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):556-572
We investigate Hilbertian Hardy type spaces of complex analytic functions of infinite many variables, associated with compact unitary groups and the corresponding invariant Haar’s measures. For such analytic functions we establish a Cauchy type integral formula and describe natural domains. Also we show some relations between constructed spaces of analytic functions and the symmetric Fock space. 相似文献
16.
《Quaestiones Mathematicae》2013,36(1-3):229-256
Abstract This is a report on a number of recent results on composition operators which map, for 0 < p ? q ∞, the Hardy space Hp (on the unit disk in the complex plane) into H q. Attention is focused on questions of boundedness (existence), compactness, order boundedness and, in connection with the latter, on relating the absolutely summing and nuclearity character as well as special factorization properties of the operator to function theoretic properties of the defining symbol. Moreover, tools are provided to show that certain classes of operators can well be distinguished already on the level of composition operators. 相似文献
17.
18.
Joel H. Shapiro 《Monatshefte für Mathematik》2000,130(1):57-70
This paper gives several different ways in which operator norms characterize those composition operators that arise from holomorphic self-maps ϕ of the unit disc that are inner functions. The setting is the Hardy space H
2 of the disc, and the key result is a characterization of inner functions in terms of the asymptotic behavior of the Nevanlinna
counting function. The case offers an interesting surprise.
(Received 25 June 1999; in revised form 29 September 1999) 相似文献
19.
V.V. Chistyakov 《Journal of Functional Analysis》2005,225(2):247-262
We prove the existence of Carathéodory-type selectors (that is, measurable in the first variable and having certain regularity properties like Lipschitz continuity, absolute continuity or bounded variation in the second variable) for multifunctions mapping the product of a measurable space and an interval into compact subsets of a metric space or metric semigroup. 相似文献
20.
Karen L. Avetisyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(2):69-73
The well-known Paley inequalities for lacunary series are applied in investigation of weighted spaces H(p, α) and H(p, log(α)) of functions holomorphic in the unit disc of the complex plane. These are spaces which are similar to the Bloch and Hardy spaces and naturally arise as the images of some fractional operators. 相似文献